analysis.special_functions.trigonometric.complex_deriv
⟷
Mathlib.Analysis.SpecialFunctions.Trigonometric.ComplexDeriv
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
-import Mathbin.Analysis.SpecialFunctions.Trigonometric.Complex
+import Analysis.SpecialFunctions.Trigonometric.Complex
#align_import analysis.special_functions.trigonometric.complex_deriv from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-
-! This file was ported from Lean 3 source module analysis.special_functions.trigonometric.complex_deriv
-! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Analysis.SpecialFunctions.Trigonometric.Complex
+#align_import analysis.special_functions.trigonometric.complex_deriv from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
+
/-!
# Complex trigonometric functions
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -28,19 +28,24 @@ open Set Filter
open scoped Real
+#print Complex.hasStrictDerivAt_tan /-
theorem hasStrictDerivAt_tan {x : ℂ} (h : cos x ≠ 0) : HasStrictDerivAt tan (1 / cos x ^ 2) x :=
by
convert (has_strict_deriv_at_sin x).div (has_strict_deriv_at_cos x) h
rw [← sin_sq_add_cos_sq x]
ring
#align complex.has_strict_deriv_at_tan Complex.hasStrictDerivAt_tan
+-/
+#print Complex.hasDerivAt_tan /-
theorem hasDerivAt_tan {x : ℂ} (h : cos x ≠ 0) : HasDerivAt tan (1 / cos x ^ 2) x :=
(hasStrictDerivAt_tan h).HasDerivAt
#align complex.has_deriv_at_tan Complex.hasDerivAt_tan
+-/
open scoped Topology
+#print Complex.tendsto_abs_tan_of_cos_eq_zero /-
theorem tendsto_abs_tan_of_cos_eq_zero {x : ℂ} (hx : cos x = 0) :
Tendsto (fun x => abs (tan x)) (𝓝[≠] x) atTop :=
by
@@ -52,12 +57,16 @@ theorem tendsto_abs_tan_of_cos_eq_zero {x : ℂ} (hx : cos x = 0) :
continuous_sin.continuous_within_at.norm.mul_at_top (norm_pos_iff.2 A)
(tendsto_norm_nhds_within_zero.comp B).inv_tendsto_zero
#align complex.tendsto_abs_tan_of_cos_eq_zero Complex.tendsto_abs_tan_of_cos_eq_zero
+-/
+#print Complex.tendsto_abs_tan_atTop /-
theorem tendsto_abs_tan_atTop (k : ℤ) :
Tendsto (fun x => abs (tan x)) (𝓝[≠] ((2 * k + 1) * π / 2)) atTop :=
tendsto_abs_tan_of_cos_eq_zero <| cos_eq_zero_iff.2 ⟨k, rfl⟩
#align complex.tendsto_abs_tan_at_top Complex.tendsto_abs_tan_atTop
+-/
+#print Complex.continuousAt_tan /-
@[simp]
theorem continuousAt_tan {x : ℂ} : ContinuousAt tan x ↔ cos x ≠ 0 :=
by
@@ -66,12 +75,16 @@ theorem continuousAt_tan {x : ℂ} : ContinuousAt tan x ↔ cos x ≠ 0 :=
not_tendsto_nhds_of_tendsto_atTop (tendsto_abs_tan_of_cos_eq_zero h₀) _
(hc.norm.tendsto.mono_left inf_le_left)
#align complex.continuous_at_tan Complex.continuousAt_tan
+-/
+#print Complex.differentiableAt_tan /-
@[simp]
theorem differentiableAt_tan {x : ℂ} : DifferentiableAt ℂ tan x ↔ cos x ≠ 0 :=
⟨fun h => continuousAt_tan.1 h.ContinuousAt, fun h => (hasDerivAt_tan h).DifferentiableAt⟩
#align complex.differentiable_at_tan Complex.differentiableAt_tan
+-/
+#print Complex.deriv_tan /-
@[simp]
theorem deriv_tan (x : ℂ) : deriv tan x = 1 / cos x ^ 2 :=
if h : cos x = 0 then
@@ -80,11 +93,14 @@ theorem deriv_tan (x : ℂ) : deriv tan x = 1 / cos x ^ 2 :=
simp [deriv_zero_of_not_differentiableAt this, h, sq]
else (hasDerivAt_tan h).deriv
#align complex.deriv_tan Complex.deriv_tan
+-/
+#print Complex.contDiffAt_tan /-
@[simp]
theorem contDiffAt_tan {x : ℂ} {n : ℕ∞} : ContDiffAt ℂ n tan x ↔ cos x ≠ 0 :=
⟨fun h => continuousAt_tan.1 h.ContinuousAt, contDiff_sin.ContDiffAt.div contDiff_cos.ContDiffAt⟩
#align complex.cont_diff_at_tan Complex.contDiffAt_tan
+-/
end Complex
mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
! This file was ported from Lean 3 source module analysis.special_functions.trigonometric.complex_deriv
-! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
+! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -13,6 +13,9 @@ import Mathbin.Analysis.SpecialFunctions.Trigonometric.Complex
/-!
# Complex trigonometric functions
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
Basic facts and derivatives for the complex trigonometric functions.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -27,7 +27,7 @@ open scoped Real
theorem hasStrictDerivAt_tan {x : ℂ} (h : cos x ≠ 0) : HasStrictDerivAt tan (1 / cos x ^ 2) x :=
by
- convert(has_strict_deriv_at_sin x).div (has_strict_deriv_at_cos x) h
+ convert (has_strict_deriv_at_sin x).div (has_strict_deriv_at_cos x) h
rw [← sin_sq_add_cos_sq x]
ring
#align complex.has_strict_deriv_at_tan Complex.hasStrictDerivAt_tan
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -23,7 +23,7 @@ namespace Complex
open Set Filter
-open Real
+open scoped Real
theorem hasStrictDerivAt_tan {x : ℂ} (h : cos x ≠ 0) : HasStrictDerivAt tan (1 / cos x ^ 2) x :=
by
@@ -36,7 +36,7 @@ theorem hasDerivAt_tan {x : ℂ} (h : cos x ≠ 0) : HasDerivAt tan (1 / cos x ^
(hasStrictDerivAt_tan h).HasDerivAt
#align complex.has_deriv_at_tan Complex.hasDerivAt_tan
-open Topology
+open scoped Topology
theorem tendsto_abs_tan_of_cos_eq_zero {x : ℂ} (hx : cos x = 0) :
Tendsto (fun x => abs (tan x)) (𝓝[≠] x) atTop :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab
@@ -4,12 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
! This file was ported from Lean 3 source module analysis.special_functions.trigonometric.complex_deriv
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
import Mathbin.Analysis.SpecialFunctions.Trigonometric.Complex
-import Mathbin.Analysis.SpecialFunctions.Trigonometric.Deriv
/-!
# Complex trigonometric functions
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d
@@ -28,7 +28,7 @@ open Real
theorem hasStrictDerivAt_tan {x : ℂ} (h : cos x ≠ 0) : HasStrictDerivAt tan (1 / cos x ^ 2) x :=
by
- convert (has_strict_deriv_at_sin x).div (has_strict_deriv_at_cos x) h
+ convert(has_strict_deriv_at_sin x).div (has_strict_deriv_at_cos x) h
rw [← sin_sq_add_cos_sq x]
ring
#align complex.has_strict_deriv_at_tan Complex.hasStrictDerivAt_tan
mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931
@@ -40,7 +40,7 @@ theorem hasDerivAt_tan {x : ℂ} (h : cos x ≠ 0) : HasDerivAt tan (1 / cos x ^
open Topology
theorem tendsto_abs_tan_of_cos_eq_zero {x : ℂ} (hx : cos x = 0) :
- Tendsto (fun x => Complex.AbsTheory.Complex.abs (tan x)) (𝓝[≠] x) atTop :=
+ Tendsto (fun x => abs (tan x)) (𝓝[≠] x) atTop :=
by
simp only [tan_eq_sin_div_cos, ← norm_eq_abs, norm_div]
have A : sin x ≠ 0 := fun h => by simpa [*, sq] using sin_sq_add_cos_sq x
@@ -52,7 +52,7 @@ theorem tendsto_abs_tan_of_cos_eq_zero {x : ℂ} (hx : cos x = 0) :
#align complex.tendsto_abs_tan_of_cos_eq_zero Complex.tendsto_abs_tan_of_cos_eq_zero
theorem tendsto_abs_tan_atTop (k : ℤ) :
- Tendsto (fun x => Complex.AbsTheory.Complex.abs (tan x)) (𝓝[≠] ((2 * k + 1) * π / 2)) atTop :=
+ Tendsto (fun x => abs (tan x)) (𝓝[≠] ((2 * k + 1) * π / 2)) atTop :=
tendsto_abs_tan_of_cos_eq_zero <| cos_eq_zero_iff.2 ⟨k, rfl⟩
#align complex.tendsto_abs_tan_at_top Complex.tendsto_abs_tan_atTop
mathlib commit https://github.com/leanprover-community/mathlib/commit/ddec54a71a0dd025c05445d467f1a2b7d586a3ba
@@ -40,7 +40,7 @@ theorem hasDerivAt_tan {x : ℂ} (h : cos x ≠ 0) : HasDerivAt tan (1 / cos x ^
open Topology
theorem tendsto_abs_tan_of_cos_eq_zero {x : ℂ} (hx : cos x = 0) :
- Tendsto (fun x => abs (tan x)) (𝓝[≠] x) atTop :=
+ Tendsto (fun x => Complex.AbsTheory.Complex.abs (tan x)) (𝓝[≠] x) atTop :=
by
simp only [tan_eq_sin_div_cos, ← norm_eq_abs, norm_div]
have A : sin x ≠ 0 := fun h => by simpa [*, sq] using sin_sq_add_cos_sq x
@@ -52,7 +52,7 @@ theorem tendsto_abs_tan_of_cos_eq_zero {x : ℂ} (hx : cos x = 0) :
#align complex.tendsto_abs_tan_of_cos_eq_zero Complex.tendsto_abs_tan_of_cos_eq_zero
theorem tendsto_abs_tan_atTop (k : ℤ) :
- Tendsto (fun x => abs (tan x)) (𝓝[≠] ((2 * k + 1) * π / 2)) atTop :=
+ Tendsto (fun x => Complex.AbsTheory.Complex.abs (tan x)) (𝓝[≠] ((2 * k + 1) * π / 2)) atTop :=
tendsto_abs_tan_of_cos_eq_zero <| cos_eq_zero_iff.2 ⟨k, rfl⟩
#align complex.tendsto_abs_tan_at_top Complex.tendsto_abs_tan_atTop
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
This is the supremum of
along with some minor fixes from failures on nightly-testing as Mathlib master
is merged into it.
Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.
I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0
branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.
In particular this includes adjustments for the Lean PRs
We can get rid of all the
local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)
macros across Mathlib (and in any projects that want to write natural number powers of reals).
Changes the default behaviour of simp
to (config := {decide := false})
. This makes simp
(and consequentially norm_num
) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp
or norm_num
to decide
or rfl
, or adding (config := {decide := true})
.
This changed the behaviour of simp
so that simp [f]
will only unfold "fully applied" occurrences of f
. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true })
. We may in future add a syntax for this, e.g. simp [!f]
; please provide feedback! In the meantime, we have made the following changes:
(config := { unfoldPartialApp := true })
in some places, to recover the old behaviour@[eqns]
to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp
and Function.flip
.This change in Lean may require further changes down the line (e.g. adding the !f
syntax, and/or upstreaming the special treatment for Function.comp
and Function.flip
, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!
Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>
@@ -16,8 +16,6 @@ Basic facts and derivatives for the complex trigonometric functions.
noncomputable section
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
namespace Complex
open Set Filter
@@ -16,7 +16,7 @@ Basic facts and derivatives for the complex trigonometric functions.
noncomputable section
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue #2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
namespace Complex
@@ -2,14 +2,11 @@
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-
-! This file was ported from Lean 3 source module analysis.special_functions.trigonometric.complex_deriv
-! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex
+#align_import analysis.special_functions.trigonometric.complex_deriv from "leanprover-community/mathlib"@"2c1d8ca2812b64f88992a5294ea3dba144755cd1"
+
/-!
# Complex trigonometric functions
The unported dependencies are
algebra.order.module
init.core
linear_algebra.free_module.finite.rank
algebra.order.monoid.cancel.defs
algebra.abs
algebra.group_power.lemmas
init.data.list.basic
linear_algebra.free_module.rank
init.data.list.default
algebra.order.monoid.cancel.basic
topology.subset_properties
init.logic
The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file