ring_theory.witt_vector.teichmuller
⟷
Mathlib.RingTheory.WittVector.Teichmuller
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) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
-import Mathbin.RingTheory.WittVector.Basic
+import RingTheory.WittVector.Basic
#align_import ring_theory.witt_vector.teichmuller from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module ring_theory.witt_vector.teichmuller
-! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.RingTheory.WittVector.Basic
+#align_import ring_theory.witt_vector.teichmuller from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
+
/-!
# Teichmüller lifts
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -40,7 +40,6 @@ open MvPolynomial
variable (p : ℕ) {R S : Type _} [hp : Fact p.Prime] [CommRing R] [CommRing S]
--- mathport name: expr𝕎
local notation "𝕎" => WittVector p
#print WittVector.teichmullerFun /-
@@ -68,8 +67,6 @@ satisfy the ring axioms.
-/
-include hp
-
private theorem ghost_component_teichmuller_fun (r : R) (n : ℕ) :
ghostComponent n (teichmullerFun p r) = r ^ p ^ n :=
by
@@ -102,6 +99,7 @@ private theorem teichmuller_mul_aux₂ (x y : MvPolynomial R ℤ) :
(MvPolynomial.map_injective _ Int.cast_injective) _
simp only [teichmuller_mul_aux₁, map_teichmuller_fun, RingHom.map_mul]
+#print WittVector.teichmuller /-
/-- The Teichmüller lift of an element of `R` to `𝕎 R`.
The `0`-th coefficient of `teichmuller p r` is `r`, and all others are `0`.
This is a monoid homomorphism. -/
@@ -117,33 +115,44 @@ def teichmuller : R →* 𝕎 R where
rcases counit_surjective R y with ⟨y, rfl⟩
simp only [← map_teichmuller_fun, ← RingHom.map_mul, teichmuller_mul_aux₂]
#align witt_vector.teichmuller WittVector.teichmuller
+-/
+#print WittVector.teichmuller_coeff_zero /-
@[simp]
theorem teichmuller_coeff_zero (r : R) : (teichmuller p r).coeff 0 = r :=
rfl
#align witt_vector.teichmuller_coeff_zero WittVector.teichmuller_coeff_zero
+-/
+#print WittVector.teichmuller_coeff_pos /-
@[simp]
theorem teichmuller_coeff_pos (r : R) : ∀ (n : ℕ) (hn : 0 < n), (teichmuller p r).coeff n = 0
| n + 1, _ => rfl
#align witt_vector.teichmuller_coeff_pos WittVector.teichmuller_coeff_pos
+-/
+#print WittVector.teichmuller_zero /-
@[simp]
theorem teichmuller_zero : teichmuller p (0 : R) = 0 := by ext ⟨⟩ <;> · rw [zero_coeff]; rfl
#align witt_vector.teichmuller_zero WittVector.teichmuller_zero
+-/
+#print WittVector.map_teichmuller /-
/-- `teichmuller` is a natural transformation. -/
@[simp]
theorem map_teichmuller (f : R →+* S) (r : R) : map f (teichmuller p r) = teichmuller p (f r) :=
map_teichmullerFun _ _ _
#align witt_vector.map_teichmuller WittVector.map_teichmuller
+-/
+#print WittVector.ghostComponent_teichmuller /-
/-- The `n`-th ghost component of `teichmuller p r` is `r ^ p ^ n`. -/
@[simp]
theorem ghostComponent_teichmuller (r : R) (n : ℕ) :
ghostComponent n (teichmuller p r) = r ^ p ^ n :=
ghostComponent_teichmullerFun _ _ _
#align witt_vector.ghost_component_teichmuller WittVector.ghostComponent_teichmuller
+-/
end WittVector
mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
! This file was ported from Lean 3 source module ring_theory.witt_vector.teichmuller
-! leanprover-community/mathlib commit c0a51cf2de54089d69301befc4c73bbc2f5c7342
+! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -13,6 +13,9 @@ import Mathbin.RingTheory.WittVector.Basic
/-!
# Teichmüller lifts
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
This file defines `witt_vector.teichmuller`, a monoid hom `R →* 𝕎 R`, which embeds `r : R` as the
`0`-th component of a Witt vector whose other coefficients are `0`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004
@@ -40,6 +40,7 @@ variable (p : ℕ) {R S : Type _} [hp : Fact p.Prime] [CommRing R] [CommRing S]
-- mathport name: expr𝕎
local notation "𝕎" => WittVector p
+#print WittVector.teichmullerFun /-
-- type as `\bbW`
/-- The underlying function of the monoid hom `witt_vector.teichmuller`.
The `0`-th coefficient of `teichmuller_fun p r` is `r`, and all others are `0`.
@@ -47,6 +48,7 @@ The `0`-th coefficient of `teichmuller_fun p r` is `r`, and all others are `0`.
def teichmullerFun (r : R) : 𝕎 R :=
⟨p, fun n => if n = 0 then r else 0⟩
#align witt_vector.teichmuller_fun WittVector.teichmullerFun
+-/
/-!
## `teichmuller` is a monoid homomorphism
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -72,22 +72,13 @@ private theorem ghost_component_teichmuller_fun (r : R) (n : ℕ) :
tsub_zero]
· rfl
· intro i hi h0
- convert MulZeroClass.mul_zero _
- convert zero_pow _
- · cases i
- · contradiction
- · rfl
+ convert MulZeroClass.mul_zero _; convert zero_pow _
+ · cases i; · contradiction; · rfl
· exact pow_pos hp.1.Pos _
- · rw [Finset.mem_range]
- intro h
- exact (h (Nat.succ_pos n)).elim
+ · rw [Finset.mem_range]; intro h; exact (h (Nat.succ_pos n)).elim
private theorem map_teichmuller_fun (f : R →+* S) (r : R) :
- map f (teichmullerFun p r) = teichmullerFun p (f r) :=
- by
- ext n
- cases n
- · rfl
+ map f (teichmullerFun p r) = teichmullerFun p (f r) := by ext n; cases n; · rfl;
· exact f.map_zero
private theorem teichmuller_mul_aux₁ (x y : MvPolynomial R ℚ) :
@@ -113,10 +104,8 @@ def teichmuller : R →* 𝕎 R where
toFun := teichmullerFun p
map_one' := by
ext ⟨⟩
- · rw [one_coeff_zero]
- rfl
- · rw [one_coeff_eq_of_pos _ _ _ (Nat.succ_pos n)]
- rfl
+ · rw [one_coeff_zero]; rfl
+ · rw [one_coeff_eq_of_pos _ _ _ (Nat.succ_pos n)]; rfl
map_mul' := by
intro x y
rcases counit_surjective R x with ⟨x, rfl⟩
@@ -135,10 +124,7 @@ theorem teichmuller_coeff_pos (r : R) : ∀ (n : ℕ) (hn : 0 < n), (teichmuller
#align witt_vector.teichmuller_coeff_pos WittVector.teichmuller_coeff_pos
@[simp]
-theorem teichmuller_zero : teichmuller p (0 : R) = 0 := by
- ext ⟨⟩ <;>
- · rw [zero_coeff]
- rfl
+theorem teichmuller_zero : teichmuller p (0 : R) = 0 := by ext ⟨⟩ <;> · rw [zero_coeff]; rfl
#align witt_vector.teichmuller_zero WittVector.teichmuller_zero
/-- `teichmuller` is a natural transformation. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -81,7 +81,6 @@ private theorem ghost_component_teichmuller_fun (r : R) (n : ℕ) :
· rw [Finset.mem_range]
intro h
exact (h (Nat.succ_pos n)).elim
-#align witt_vector.ghost_component_teichmuller_fun witt_vector.ghost_component_teichmuller_fun
private theorem map_teichmuller_fun (f : R →+* S) (r : R) :
map f (teichmullerFun p r) = teichmullerFun p (f r) :=
@@ -90,7 +89,6 @@ private theorem map_teichmuller_fun (f : R →+* S) (r : R) :
cases n
· rfl
· exact f.map_zero
-#align witt_vector.map_teichmuller_fun witt_vector.map_teichmuller_fun
private theorem teichmuller_mul_aux₁ (x y : MvPolynomial R ℚ) :
teichmullerFun p (x * y) = teichmullerFun p x * teichmullerFun p y :=
@@ -99,7 +97,6 @@ private theorem teichmuller_mul_aux₁ (x y : MvPolynomial R ℚ) :
rw [RingHom.map_mul]
ext1 n
simp only [Pi.mul_apply, ghost_map_apply, ghost_component_teichmuller_fun, mul_pow]
-#align witt_vector.teichmuller_mul_aux₁ witt_vector.teichmuller_mul_aux₁
private theorem teichmuller_mul_aux₂ (x y : MvPolynomial R ℤ) :
teichmullerFun p (x * y) = teichmullerFun p x * teichmullerFun p y :=
@@ -108,7 +105,6 @@ private theorem teichmuller_mul_aux₂ (x y : MvPolynomial R ℤ) :
map_injective (MvPolynomial.map (Int.castRingHom ℚ))
(MvPolynomial.map_injective _ Int.cast_injective) _
simp only [teichmuller_mul_aux₁, map_teichmuller_fun, RingHom.map_mul]
-#align witt_vector.teichmuller_mul_aux₂ witt_vector.teichmuller_mul_aux₂
/-- The Teichmüller lift of an element of `R` to `𝕎 R`.
The `0`-th coefficient of `teichmuller p r` is `r`, and all others are `0`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212
@@ -72,7 +72,7 @@ private theorem ghost_component_teichmuller_fun (r : R) (n : ℕ) :
tsub_zero]
· rfl
· intro i hi h0
- convert mul_zero _
+ convert MulZeroClass.mul_zero _
convert zero_pow _
· cases i
· contradiction
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
f ^ n
(#9617)
This involves moving lemmas from Algebra.GroupPower.Ring
to Algebra.GroupWithZero.Basic
and changing some 0 < n
assumptions to n ≠ 0
.
From LeanAPAP
@@ -63,13 +63,8 @@ private theorem ghostComponent_teichmullerFun (r : R) (n : ℕ) :
rw [ghostComponent_apply, aeval_wittPolynomial, Finset.sum_eq_single 0, pow_zero, one_mul,
tsub_zero]
· rfl
- · intro i hi h0
- convert mul_zero (M₀ := R) _
- convert zero_pow (M := R) _
- · cases i
- · contradiction
- · rfl
- · exact pow_pos hp.1.pos _
+ · intro i _ h0
+ simp [teichmullerFun, h0, hp.1.ne_zero]
· rw [Finset.mem_range]; intro h; exact (h (Nat.succ_pos n)).elim
private theorem map_teichmullerFun (f : R →+* S) (r : R) :
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -32,7 +32,7 @@ namespace WittVector
open MvPolynomial
-variable (p : ℕ) {R S : Type _} [hp : Fact p.Prime] [CommRing R] [CommRing S]
+variable (p : ℕ) {R S : Type*} [hp : Fact p.Prime] [CommRing R] [CommRing S]
local notation "𝕎" => WittVector p -- type as `\bbW`
@@ -2,14 +2,11 @@
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module ring_theory.witt_vector.teichmuller
-! leanprover-community/mathlib commit c0a51cf2de54089d69301befc4c73bbc2f5c7342
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.RingTheory.WittVector.Basic
+#align_import ring_theory.witt_vector.teichmuller from "leanprover-community/mathlib"@"c0a51cf2de54089d69301befc4c73bbc2f5c7342"
+
/-!
# Teichmüller lifts
The unported dependencies are