mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -99,11 +99,11 @@ theorem isIntegralClosure_adjoin_singleton_of_prime_pow [hcycl : IsCyclotomicExt
   have hint : IsIntegral ℤ B.gen := IsIntegral.sub (hζ.is_integral (p ^ k).Pos) isIntegral_one
   have H := discr_mul_is_integral_mem_adjoin ℚ hint h
   obtain ⟨u, n, hun⟩ := discr_prime_pow_eq_unit_mul_pow' hζ
-  rw [hun] at H 
+  rw [hun] at H
   replace H := Subalgebra.smul_mem _ H u.inv
   rw [← smul_assoc, ← smul_mul_assoc, Units.inv_eq_val_inv, coe_coe, zsmul_eq_mul, ← Int.cast_mul,
     Units.inv_mul, Int.cast_one, one_mul,
-    show (p : ℚ) ^ n • x = ((p : ℕ) : ℤ) ^ n • x by simp [smul_def]] at H 
+    show (p : ℚ) ^ n • x = ((p : ℕ) : ℤ) ^ n • x by simp [smul_def]] at H
   cases k
   · haveI : IsCyclotomicExtension {1} ℚ K := by simpa using hcycl
     have : x ∈ (⊥ : Subalgebra ℚ K) := by
@@ -118,9 +118,9 @@ theorem isIntegralClosure_adjoin_singleton_of_prime_pow [hcycl : IsCyclotomicExt
       by
       have h₁ := minpoly.isIntegrallyClosed_eq_field_fractions' ℚ hint
       have h₂ := hζ.minpoly_sub_one_eq_cyclotomic_comp (cyclotomic.irreducible_rat (p ^ _).Pos)
-      rw [IsPrimitiveRoot.subOnePowerBasis_gen] at h₁ 
+      rw [IsPrimitiveRoot.subOnePowerBasis_gen] at h₁
       rw [h₁, ← map_cyclotomic_int, show Int.castRingHom ℚ = algebraMap ℤ ℚ by rfl,
-        show X + 1 = map (algebraMap ℤ ℚ) (X + 1) by simp, ← map_comp] at h₂ 
+        show X + 1 = map (algebraMap ℤ ℚ) (X + 1) by simp, ← map_comp] at h₂
       haveI : CharZero ℚ := StrictOrderedSemiring.to_charZero
       rw [IsPrimitiveRoot.subOnePowerBasis_gen,
         map_injective (algebraMap ℤ ℚ) (algebraMap ℤ ℚ).injective_int h₂]
@@ -138,7 +138,7 @@ theorem isIntegralClosure_adjoin_singleton_of_prime_pow [hcycl : IsCyclotomicExt
 theorem isIntegralClosure_adjoin_singleton_of_prime [hcycl : IsCyclotomicExtension {p} ℚ K]
     (hζ : IsPrimitiveRoot ζ ↑p) : IsIntegralClosure (adjoin ℤ ({ζ} : Set K)) ℤ K :=
   by
-  rw [← pow_one p] at hζ hcycl 
+  rw [← pow_one p] at hζ hcycl
   exact is_integral_closure_adjoin_singleton_of_prime_pow hζ
 #align is_cyclotomic_extension.rat.is_integral_closure_adjoin_singleton_of_prime IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -96,7 +96,7 @@ theorem isIntegralClosure_adjoin_singleton_of_prime_pow [hcycl : IsCyclotomicExt
         (le_integralClosure_iff_isIntegral.1
           (adjoin_le_integralClosure (hζ.is_integral (p ^ k).Pos)) _)
   let B := hζ.sub_one_power_basis ℚ
-  have hint : IsIntegral ℤ B.gen := isIntegral_sub (hζ.is_integral (p ^ k).Pos) isIntegral_one
+  have hint : IsIntegral ℤ B.gen := IsIntegral.sub (hζ.is_integral (p ^ k).Pos) isIntegral_one
   have H := discr_mul_is_integral_mem_adjoin ℚ hint h
   obtain ⟨u, n, hun⟩ := discr_prime_pow_eq_unit_mul_pow' hζ
   rw [hun] at H 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,8 +3,8 @@ Copyright (c) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 -/
-import Mathbin.NumberTheory.Cyclotomic.Discriminant
-import Mathbin.RingTheory.Polynomial.Eisenstein.IsIntegral
+import NumberTheory.Cyclotomic.Discriminant
+import RingTheory.Polynomial.Eisenstein.IsIntegral
 
 #align_import number_theory.cyclotomic.rat from "leanprover-community/mathlib"@"30faa0c3618ce1472bf6305ae0e3fa56affa3f95"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
-
-! This file was ported from Lean 3 source module number_theory.cyclotomic.rat
-! leanprover-community/mathlib commit 30faa0c3618ce1472bf6305ae0e3fa56affa3f95
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.NumberTheory.Cyclotomic.Discriminant
 import Mathbin.RingTheory.Polynomial.Eisenstein.IsIntegral
 
+#align_import number_theory.cyclotomic.rat from "leanprover-community/mathlib"@"30faa0c3618ce1472bf6305ae0e3fa56affa3f95"
+
 /-!
 # Ring of integers of `p ^ n`-th cyclotomic fields
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 
 ! This file was ported from Lean 3 source module number_theory.cyclotomic.rat
-! leanprover-community/mathlib commit b353176c24d96c23f0ce1cc63efc3f55019702d9
+! leanprover-community/mathlib commit 30faa0c3618ce1472bf6305ae0e3fa56affa3f95
 ! 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.Polynomial.Eisenstein.IsIntegral
 
 /-!
 # Ring of integers of `p ^ n`-th cyclotomic fields
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 We gather results about cyclotomic extensions of `ℚ`. In particular, we compute the ring of
 integers of a `p ^ n`-th cyclotomic extension of `ℚ`.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/fdc286cc6967a012f41b87f76dcd2797b53152af

@@ -124,10 +124,10 @@ theorem isIntegralClosure_adjoin_singleton_of_prime_pow [hcycl : IsCyclotomicExt
       haveI : CharZero ℚ := StrictOrderedSemiring.to_charZero
       rw [IsPrimitiveRoot.subOnePowerBasis_gen,
         map_injective (algebraMap ℤ ℚ) (algebraMap ℤ ℚ).injective_int h₂]
-      exact cyclotomic_prime_pow_comp_x_add_one_isEisensteinAt _ _
+      exact cyclotomic_prime_pow_comp_X_add_one_isEisensteinAt _ _
     refine'
       adjoin_le _
-        (mem_adjoin_of_smul_prime_pow_smul_of_minpoly_is_eiseinstein_at
+        (mem_adjoin_of_smul_prime_pow_smul_of_minpoly_isEisensteinAt
           (Nat.prime_iff_prime_int.1 hp.out) hint h H hmin)
     simp only [Set.singleton_subset_iff, SetLike.mem_coe]
     exact Subalgebra.sub_mem _ (self_mem_adjoin_singleton ℤ _) (Subalgebra.one_mem _)

mathlib commit https://github.com/leanprover-community/mathlib/commit/93f880918cb51905fd51b76add8273cbc27718ab

@@ -35,6 +35,7 @@ variable {p : ℕ+} {k : ℕ} {K : Type u} [Field K] [CharZero K] {ζ : K} [hp :
 
 namespace IsCyclotomicExtension.Rat
 
+#print IsCyclotomicExtension.Rat.discr_prime_pow_ne_two' /-
 /-- The discriminant of the power basis given by `ζ - 1`. -/
 theorem discr_prime_pow_ne_two' [IsCyclotomicExtension {p ^ (k + 1)} ℚ K]
     (hζ : IsPrimitiveRoot ζ ↑(p ^ (k + 1))) (hk : p ^ (k + 1) ≠ 2) :
@@ -44,14 +45,18 @@ theorem discr_prime_pow_ne_two' [IsCyclotomicExtension {p ^ (k + 1)} ℚ K]
   rw [← discr_prime_pow_ne_two hζ (cyclotomic.irreducible_rat (p ^ (k + 1)).Pos) hk]
   exact hζ.discr_zeta_eq_discr_zeta_sub_one.symm
 #align is_cyclotomic_extension.rat.discr_prime_pow_ne_two' IsCyclotomicExtension.Rat.discr_prime_pow_ne_two'
+-/
 
+#print IsCyclotomicExtension.Rat.discr_odd_prime' /-
 theorem discr_odd_prime' [IsCyclotomicExtension {p} ℚ K] (hζ : IsPrimitiveRoot ζ p) (hodd : p ≠ 2) :
     discr ℚ (hζ.subOnePowerBasis ℚ).basis = (-1) ^ (((p : ℕ) - 1) / 2) * p ^ ((p : ℕ) - 2) :=
   by
   rw [← discr_odd_prime hζ (cyclotomic.irreducible_rat hp.out.pos) hodd]
   exact hζ.discr_zeta_eq_discr_zeta_sub_one.symm
 #align is_cyclotomic_extension.rat.discr_odd_prime' IsCyclotomicExtension.Rat.discr_odd_prime'
+-/
 
+#print IsCyclotomicExtension.Rat.discr_prime_pow' /-
 /-- The discriminant of the power basis given by `ζ - 1`. Beware that in the cases `p ^ k = 1` and
 `p ^ k = 2` the formula uses `1 / 2 = 0` and `0 - 1 = 0`. It is useful only to have a uniform
 result. See also `is_cyclotomic_extension.rat.discr_prime_pow_eq_unit_mul_pow'`. -/
@@ -62,7 +67,9 @@ theorem discr_prime_pow' [IsCyclotomicExtension {p ^ k} ℚ K] (hζ : IsPrimitiv
   rw [← discr_prime_pow hζ (cyclotomic.irreducible_rat (p ^ k).Pos)]
   exact hζ.discr_zeta_eq_discr_zeta_sub_one.symm
 #align is_cyclotomic_extension.rat.discr_prime_pow' IsCyclotomicExtension.Rat.discr_prime_pow'
+-/
 
+#print IsCyclotomicExtension.Rat.discr_prime_pow_eq_unit_mul_pow' /-
 /-- If `p` is a prime and `is_cyclotomic_extension {p ^ k} K L`, then there are `u : ℤˣ` and
 `n : ℕ` such that the discriminant of the power basis given by `ζ - 1` is `u * p ^ n`. Often this is
 enough and less cumbersome to use than `is_cyclotomic_extension.rat.discr_prime_pow'`. -/
@@ -73,7 +80,9 @@ theorem discr_prime_pow_eq_unit_mul_pow' [IsCyclotomicExtension {p ^ k} ℚ K]
   rw [hζ.discr_zeta_eq_discr_zeta_sub_one.symm]
   exact discr_prime_pow_eq_unit_mul_pow hζ (cyclotomic.irreducible_rat (p ^ k).Pos)
 #align is_cyclotomic_extension.rat.discr_prime_pow_eq_unit_mul_pow' IsCyclotomicExtension.Rat.discr_prime_pow_eq_unit_mul_pow'
+-/
 
+#print IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime_pow /-
 /-- If `K` is a `p ^ k`-th cyclotomic extension of `ℚ`, then `(adjoin ℤ {ζ})` is the
 integral closure of `ℤ` in `K`. -/
 theorem isIntegralClosure_adjoin_singleton_of_prime_pow [hcycl : IsCyclotomicExtension {p ^ k} ℚ K]
@@ -123,14 +132,18 @@ theorem isIntegralClosure_adjoin_singleton_of_prime_pow [hcycl : IsCyclotomicExt
     simp only [Set.singleton_subset_iff, SetLike.mem_coe]
     exact Subalgebra.sub_mem _ (self_mem_adjoin_singleton ℤ _) (Subalgebra.one_mem _)
 #align is_cyclotomic_extension.rat.is_integral_closure_adjoin_singleton_of_prime_pow IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime_pow
+-/
 
+#print IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime /-
 theorem isIntegralClosure_adjoin_singleton_of_prime [hcycl : IsCyclotomicExtension {p} ℚ K]
     (hζ : IsPrimitiveRoot ζ ↑p) : IsIntegralClosure (adjoin ℤ ({ζ} : Set K)) ℤ K :=
   by
   rw [← pow_one p] at hζ hcycl 
   exact is_integral_closure_adjoin_singleton_of_prime_pow hζ
 #align is_cyclotomic_extension.rat.is_integral_closure_adjoin_singleton_of_prime IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime
+-/
 
+#print IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure_of_prime_pow /-
 /-- The integral closure of `ℤ` inside `cyclotomic_field (p ^ k) ℚ` is
 `cyclotomic_ring (p ^ k) ℤ ℚ`. -/
 theorem cyclotomicRing_isIntegralClosure_of_prime_pow :
@@ -147,13 +160,16 @@ theorem cyclotomicRing_isIntegralClosure_of_prime_pow :
   · rintro ⟨y, rfl⟩
     exact IsIntegral.algebraMap ((IsCyclotomicExtension.integral {p ^ k} ℤ _) _)
 #align is_cyclotomic_extension.rat.cyclotomic_ring_is_integral_closure_of_prime_pow IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure_of_prime_pow
+-/
 
+#print IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure_of_prime /-
 theorem cyclotomicRing_isIntegralClosure_of_prime :
     IsIntegralClosure (CyclotomicRing p ℤ ℚ) ℤ (CyclotomicField p ℚ) :=
   by
   rw [← pow_one p]
   exact cyclotomic_ring_is_integral_closure_of_prime_pow
 #align is_cyclotomic_extension.rat.cyclotomic_ring_is_integral_closure_of_prime IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure_of_prime
+-/
 
 end IsCyclotomicExtension.Rat
 
@@ -163,6 +179,7 @@ open IsCyclotomicExtension.Rat
 
 namespace IsPrimitiveRoot
 
+#print IsPrimitiveRoot.adjoinEquivRingOfIntegers /-
 /-- The algebra isomorphism `adjoin ℤ {ζ} ≃ₐ[ℤ] (𝓞 K)`, where `ζ` is a primitive `p ^ k`-th root of
 unity and `K` is a `p ^ k`-th cyclotomic extension of `ℚ`. -/
 @[simps]
@@ -172,34 +189,44 @@ noncomputable def IsPrimitiveRoot.adjoinEquivRingOfIntegers
   let _ := isIntegralClosure_adjoin_singleton_of_prime_pow hζ
   IsIntegralClosure.equiv ℤ (adjoin ℤ ({ζ} : Set K)) K (𝓞 K)
 #align is_primitive_root.adjoin_equiv_ring_of_integers IsPrimitiveRoot.adjoinEquivRingOfIntegers
+-/
 
+#print IsPrimitiveRoot.IsCyclotomicExtension.ringOfIntegers /-
 /-- The ring of integers of a `p ^ k`-th cyclotomic extension of `ℚ` is a cyclotomic extension. -/
-instance IsCyclotomicExtension.ringOfIntegers [IsCyclotomicExtension {p ^ k} ℚ K] :
+instance IsPrimitiveRoot.IsCyclotomicExtension.ringOfIntegers [IsCyclotomicExtension {p ^ k} ℚ K] :
     IsCyclotomicExtension {p ^ k} ℤ (𝓞 K) :=
   let _ := (zeta_spec (p ^ k) ℚ K).adjoin_isCyclotomicExtension ℤ
   IsCyclotomicExtension.equiv _ ℤ _ (zeta_spec (p ^ k) ℚ K).adjoinEquivRingOfIntegers
-#align is_cyclotomic_extension.ring_of_integers IsCyclotomicExtension.ringOfIntegers
+#align is_cyclotomic_extension.ring_of_integers IsPrimitiveRoot.IsCyclotomicExtension.ringOfIntegers
+-/
 
+#print IsPrimitiveRoot.integralPowerBasis /-
 /-- The integral `power_basis` of `𝓞 K` given by a primitive root of unity, where `K` is a `p ^ k`
 cyclotomic extension of `ℚ`. -/
 noncomputable def integralPowerBasis [hcycl : IsCyclotomicExtension {p ^ k} ℚ K]
     (hζ : IsPrimitiveRoot ζ ↑(p ^ k)) : PowerBasis ℤ (𝓞 K) :=
   (adjoin.powerBasis' (hζ.IsIntegral (p ^ k).Pos)).map hζ.adjoinEquivRingOfIntegers
 #align is_primitive_root.integral_power_basis IsPrimitiveRoot.integralPowerBasis
+-/
 
+#print IsPrimitiveRoot.integralPowerBasis_gen /-
 @[simp]
 theorem integralPowerBasis_gen [hcycl : IsCyclotomicExtension {p ^ k} ℚ K]
     (hζ : IsPrimitiveRoot ζ ↑(p ^ k)) :
     hζ.integralPowerBasis.gen = ⟨ζ, hζ.IsIntegral (p ^ k).Pos⟩ :=
   Subtype.ext <| show algebraMap _ K hζ.integralPowerBasis.gen = _ by simpa [integral_power_basis]
 #align is_primitive_root.integral_power_basis_gen IsPrimitiveRoot.integralPowerBasis_gen
+-/
 
+#print IsPrimitiveRoot.integralPowerBasis_dim /-
 @[simp]
 theorem integralPowerBasis_dim [hcycl : IsCyclotomicExtension {p ^ k} ℚ K]
     (hζ : IsPrimitiveRoot ζ ↑(p ^ k)) : hζ.integralPowerBasis.dim = φ (p ^ k) := by
   simp [integral_power_basis, ← cyclotomic_eq_minpoly hζ, nat_degree_cyclotomic]
 #align is_primitive_root.integral_power_basis_dim IsPrimitiveRoot.integralPowerBasis_dim
+-/
 
+#print IsPrimitiveRoot.adjoinEquivRingOfIntegers' /-
 /-- The algebra isomorphism `adjoin ℤ {ζ} ≃ₐ[ℤ] (𝓞 K)`, where `ζ` is a primitive `p`-th root of
 unity and `K` is a `p`-th cyclotomic extension of `ℚ`. -/
 @[simps]
@@ -207,34 +234,44 @@ noncomputable def IsPrimitiveRoot.adjoinEquivRingOfIntegers' [hcycl : IsCyclotom
     (hζ : IsPrimitiveRoot ζ p) : adjoin ℤ ({ζ} : Set K) ≃ₐ[ℤ] 𝓞 K :=
   @adjoinEquivRingOfIntegers p 1 K _ _ _ _ (by convert hcycl; rw [pow_one]) (by rwa [pow_one])
 #align is_primitive_root.adjoin_equiv_ring_of_integers' IsPrimitiveRoot.adjoinEquivRingOfIntegers'
+-/
 
+#print IsCyclotomicExtension.ring_of_integers' /-
 /-- The ring of integers of a `p`-th cyclotomic extension of `ℚ` is a cyclotomic extension. -/
 instance IsCyclotomicExtension.ring_of_integers' [IsCyclotomicExtension {p} ℚ K] :
     IsCyclotomicExtension {p} ℤ (𝓞 K) :=
   let _ := (zeta_spec p ℚ K).adjoin_isCyclotomicExtension ℤ
   IsCyclotomicExtension.equiv _ ℤ _ (zeta_spec p ℚ K).adjoinEquivRingOfIntegers'
 #align is_cyclotomic_extension.ring_of_integers' IsCyclotomicExtension.ring_of_integers'
+-/
 
+#print IsPrimitiveRoot.integralPowerBasis' /-
 /-- The integral `power_basis` of `𝓞 K` given by a primitive root of unity, where `K` is a `p`-th
 cyclotomic extension of `ℚ`. -/
 noncomputable def integralPowerBasis' [hcycl : IsCyclotomicExtension {p} ℚ K]
     (hζ : IsPrimitiveRoot ζ p) : PowerBasis ℤ (𝓞 K) :=
   @integralPowerBasis p 1 K _ _ _ _ (by convert hcycl; rw [pow_one]) (by rwa [pow_one])
 #align is_primitive_root.integral_power_basis' IsPrimitiveRoot.integralPowerBasis'
+-/
 
+#print IsPrimitiveRoot.integralPowerBasis'_gen /-
 @[simp]
 theorem integralPowerBasis'_gen [hcycl : IsCyclotomicExtension {p} ℚ K] (hζ : IsPrimitiveRoot ζ p) :
     hζ.integralPowerBasis'.gen = ⟨ζ, hζ.IsIntegral p.Pos⟩ :=
   @integralPowerBasis_gen p 1 K _ _ _ _ (by convert hcycl; rw [pow_one]) (by rwa [pow_one])
 #align is_primitive_root.integral_power_basis'_gen IsPrimitiveRoot.integralPowerBasis'_gen
+-/
 
+#print IsPrimitiveRoot.power_basis_int'_dim /-
 @[simp]
 theorem power_basis_int'_dim [hcycl : IsCyclotomicExtension {p} ℚ K] (hζ : IsPrimitiveRoot ζ p) :
     hζ.integralPowerBasis'.dim = φ p := by
   erw [@integral_power_basis_dim p 1 K _ _ _ _ (by convert hcycl; rw [pow_one]) (by rwa [pow_one]),
     pow_one]
 #align is_primitive_root.power_basis_int'_dim IsPrimitiveRoot.power_basis_int'_dim
+-/
 
+#print IsPrimitiveRoot.subOneIntegralPowerBasis /-
 /-- The integral `power_basis` of `𝓞 K` given by `ζ - 1`, where `K` is a `p ^ k` cyclotomic
 extension of `ℚ`. -/
 noncomputable def subOneIntegralPowerBasis [IsCyclotomicExtension {p ^ k} ℚ K]
@@ -248,7 +285,9 @@ noncomputable def subOneIntegralPowerBasis [IsCyclotomicExtension {p ^ k} ℚ K]
         Subalgebra.add_mem _ (self_mem_adjoin_singleton ℤ (⟨ζ - 1, _⟩ : 𝓞 K)) (Subalgebra.one_mem _)
       simp)
 #align is_primitive_root.sub_one_integral_power_basis IsPrimitiveRoot.subOneIntegralPowerBasis
+-/
 
+#print IsPrimitiveRoot.subOneIntegralPowerBasis_gen /-
 @[simp]
 theorem subOneIntegralPowerBasis_gen [IsCyclotomicExtension {p ^ k} ℚ K]
     (hζ : IsPrimitiveRoot ζ ↑(p ^ k)) :
@@ -256,14 +295,18 @@ theorem subOneIntegralPowerBasis_gen [IsCyclotomicExtension {p ^ k} ℚ K]
       ⟨ζ - 1, Subalgebra.sub_mem _ (hζ.IsIntegral (p ^ k).Pos) (Subalgebra.one_mem _)⟩ :=
   by simp [sub_one_integral_power_basis]
 #align is_primitive_root.sub_one_integral_power_basis_gen IsPrimitiveRoot.subOneIntegralPowerBasis_gen
+-/
 
+#print IsPrimitiveRoot.subOneIntegralPowerBasis' /-
 /-- The integral `power_basis` of `𝓞 K` given by `ζ - 1`, where `K` is a `p`-th cyclotomic
 extension of `ℚ`. -/
 noncomputable def subOneIntegralPowerBasis' [hcycl : IsCyclotomicExtension {p} ℚ K]
     (hζ : IsPrimitiveRoot ζ p) : PowerBasis ℤ (𝓞 K) :=
   @subOneIntegralPowerBasis p 1 K _ _ _ _ (by convert hcycl; rw [pow_one]) (by rwa [pow_one])
 #align is_primitive_root.sub_one_integral_power_basis' IsPrimitiveRoot.subOneIntegralPowerBasis'
+-/
 
+#print IsPrimitiveRoot.subOneIntegralPowerBasis'_gen /-
 @[simp]
 theorem subOneIntegralPowerBasis'_gen [hcycl : IsCyclotomicExtension {p} ℚ K]
     (hζ : IsPrimitiveRoot ζ p) :
@@ -271,6 +314,7 @@ theorem subOneIntegralPowerBasis'_gen [hcycl : IsCyclotomicExtension {p} ℚ K]
       ⟨ζ - 1, Subalgebra.sub_mem _ (hζ.IsIntegral p.Pos) (Subalgebra.one_mem _)⟩ :=
   @subOneIntegralPowerBasis_gen p 1 K _ _ _ _ (by convert hcycl; rw [pow_one]) (by rwa [pow_one])
 #align is_primitive_root.sub_one_integral_power_basis'_gen IsPrimitiveRoot.subOneIntegralPowerBasis'_gen
+-/
 
 end IsPrimitiveRoot
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/d30d31261cdb4d2f5e612eabc3c4bf45556350d5

@@ -184,7 +184,7 @@ instance IsCyclotomicExtension.ringOfIntegers [IsCyclotomicExtension {p ^ k} ℚ
 cyclotomic extension of `ℚ`. -/
 noncomputable def integralPowerBasis [hcycl : IsCyclotomicExtension {p ^ k} ℚ K]
     (hζ : IsPrimitiveRoot ζ ↑(p ^ k)) : PowerBasis ℤ (𝓞 K) :=
-  (minpoly.Algebra.adjoin.powerBasis' (hζ.IsIntegral (p ^ k).Pos)).map hζ.adjoinEquivRingOfIntegers
+  (adjoin.powerBasis' (hζ.IsIntegral (p ^ k).Pos)).map hζ.adjoinEquivRingOfIntegers
 #align is_primitive_root.integral_power_basis IsPrimitiveRoot.integralPowerBasis
 
 @[simp]
@@ -239,7 +239,7 @@ theorem power_basis_int'_dim [hcycl : IsCyclotomicExtension {p} ℚ K] (hζ : Is
 extension of `ℚ`. -/
 noncomputable def subOneIntegralPowerBasis [IsCyclotomicExtension {p ^ k} ℚ K]
     (hζ : IsPrimitiveRoot ζ ↑(p ^ k)) : PowerBasis ℤ (𝓞 K) :=
-  minpoly.PowerBasis.ofGenMemAdjoin' hζ.integralPowerBasis
+  PowerBasis.ofGenMemAdjoin' hζ.integralPowerBasis
     (isIntegral_of_mem_ringOfIntegers <|
       Subalgebra.sub_mem _ (hζ.IsIntegral (p ^ k).Pos) (Subalgebra.one_mem _))
     (by

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -184,7 +184,7 @@ instance IsCyclotomicExtension.ringOfIntegers [IsCyclotomicExtension {p ^ k} ℚ
 cyclotomic extension of `ℚ`. -/
 noncomputable def integralPowerBasis [hcycl : IsCyclotomicExtension {p ^ k} ℚ K]
     (hζ : IsPrimitiveRoot ζ ↑(p ^ k)) : PowerBasis ℤ (𝓞 K) :=
-  (adjoin.powerBasis' (hζ.IsIntegral (p ^ k).Pos)).map hζ.adjoinEquivRingOfIntegers
+  (minpoly.Algebra.adjoin.powerBasis' (hζ.IsIntegral (p ^ k).Pos)).map hζ.adjoinEquivRingOfIntegers
 #align is_primitive_root.integral_power_basis IsPrimitiveRoot.integralPowerBasis
 
 @[simp]
@@ -239,7 +239,7 @@ theorem power_basis_int'_dim [hcycl : IsCyclotomicExtension {p} ℚ K] (hζ : Is
 extension of `ℚ`. -/
 noncomputable def subOneIntegralPowerBasis [IsCyclotomicExtension {p ^ k} ℚ K]
     (hζ : IsPrimitiveRoot ζ ↑(p ^ k)) : PowerBasis ℤ (𝓞 K) :=
-  PowerBasis.ofGenMemAdjoin' hζ.integralPowerBasis
+  minpoly.PowerBasis.ofGenMemAdjoin' hζ.integralPowerBasis
     (isIntegral_of_mem_ringOfIntegers <|
       Subalgebra.sub_mem _ (hζ.IsIntegral (p ^ k).Pos) (Subalgebra.one_mem _))
     (by

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -33,8 +33,6 @@ open scoped Cyclotomic NumberField Nat
 
 variable {p : ℕ+} {k : ℕ} {K : Type u} [Field K] [CharZero K] {ζ : K} [hp : Fact (p : ℕ).Prime]
 
-include hp
-
 namespace IsCyclotomicExtension.Rat
 
 /-- The discriminant of the power basis given by `ζ - 1`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -246,8 +246,8 @@ noncomputable def subOneIntegralPowerBasis [IsCyclotomicExtension {p ^ k} ℚ K]
       Subalgebra.sub_mem _ (hζ.IsIntegral (p ^ k).Pos) (Subalgebra.one_mem _))
     (by
       simp only [integral_power_basis_gen]
-      convert Subalgebra.add_mem _ (self_mem_adjoin_singleton ℤ (⟨ζ - 1, _⟩ : 𝓞 K))
-          (Subalgebra.one_mem _)
+      convert
+        Subalgebra.add_mem _ (self_mem_adjoin_singleton ℤ (⟨ζ - 1, _⟩ : 𝓞 K)) (Subalgebra.one_mem _)
       simp)
 #align is_primitive_root.sub_one_integral_power_basis IsPrimitiveRoot.subOneIntegralPowerBasis
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -70,7 +70,7 @@ theorem discr_prime_pow' [IsCyclotomicExtension {p ^ k} ℚ K] (hζ : IsPrimitiv
 enough and less cumbersome to use than `is_cyclotomic_extension.rat.discr_prime_pow'`. -/
 theorem discr_prime_pow_eq_unit_mul_pow' [IsCyclotomicExtension {p ^ k} ℚ K]
     (hζ : IsPrimitiveRoot ζ ↑(p ^ k)) :
-    ∃ (u : ℤˣ)(n : ℕ), discr ℚ (hζ.subOnePowerBasis ℚ).basis = u * p ^ n :=
+    ∃ (u : ℤˣ) (n : ℕ), discr ℚ (hζ.subOnePowerBasis ℚ).basis = u * p ^ n :=
   by
   rw [hζ.discr_zeta_eq_discr_zeta_sub_one.symm]
   exact discr_prime_pow_eq_unit_mul_pow hζ (cyclotomic.irreducible_rat (p ^ k).Pos)
@@ -92,11 +92,11 @@ theorem isIntegralClosure_adjoin_singleton_of_prime_pow [hcycl : IsCyclotomicExt
   have hint : IsIntegral ℤ B.gen := isIntegral_sub (hζ.is_integral (p ^ k).Pos) isIntegral_one
   have H := discr_mul_is_integral_mem_adjoin ℚ hint h
   obtain ⟨u, n, hun⟩ := discr_prime_pow_eq_unit_mul_pow' hζ
-  rw [hun] at H
+  rw [hun] at H 
   replace H := Subalgebra.smul_mem _ H u.inv
   rw [← smul_assoc, ← smul_mul_assoc, Units.inv_eq_val_inv, coe_coe, zsmul_eq_mul, ← Int.cast_mul,
     Units.inv_mul, Int.cast_one, one_mul,
-    show (p : ℚ) ^ n • x = ((p : ℕ) : ℤ) ^ n • x by simp [smul_def]] at H
+    show (p : ℚ) ^ n • x = ((p : ℕ) : ℤ) ^ n • x by simp [smul_def]] at H 
   cases k
   · haveI : IsCyclotomicExtension {1} ℚ K := by simpa using hcycl
     have : x ∈ (⊥ : Subalgebra ℚ K) := by
@@ -111,9 +111,9 @@ theorem isIntegralClosure_adjoin_singleton_of_prime_pow [hcycl : IsCyclotomicExt
       by
       have h₁ := minpoly.isIntegrallyClosed_eq_field_fractions' ℚ hint
       have h₂ := hζ.minpoly_sub_one_eq_cyclotomic_comp (cyclotomic.irreducible_rat (p ^ _).Pos)
-      rw [IsPrimitiveRoot.subOnePowerBasis_gen] at h₁
+      rw [IsPrimitiveRoot.subOnePowerBasis_gen] at h₁ 
       rw [h₁, ← map_cyclotomic_int, show Int.castRingHom ℚ = algebraMap ℤ ℚ by rfl,
-        show X + 1 = map (algebraMap ℤ ℚ) (X + 1) by simp, ← map_comp] at h₂
+        show X + 1 = map (algebraMap ℤ ℚ) (X + 1) by simp, ← map_comp] at h₂ 
       haveI : CharZero ℚ := StrictOrderedSemiring.to_charZero
       rw [IsPrimitiveRoot.subOnePowerBasis_gen,
         map_injective (algebraMap ℤ ℚ) (algebraMap ℤ ℚ).injective_int h₂]
@@ -129,7 +129,7 @@ theorem isIntegralClosure_adjoin_singleton_of_prime_pow [hcycl : IsCyclotomicExt
 theorem isIntegralClosure_adjoin_singleton_of_prime [hcycl : IsCyclotomicExtension {p} ℚ K]
     (hζ : IsPrimitiveRoot ζ ↑p) : IsIntegralClosure (adjoin ℤ ({ζ} : Set K)) ℤ K :=
   by
-  rw [← pow_one p] at hζ hcycl
+  rw [← pow_one p] at hζ hcycl 
   exact is_integral_closure_adjoin_singleton_of_prime_pow hζ
 #align is_cyclotomic_extension.rat.is_integral_closure_adjoin_singleton_of_prime IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -29,7 +29,7 @@ universe u
 
 open Algebra IsCyclotomicExtension Polynomial NumberField
 
-open Cyclotomic NumberField Nat
+open scoped Cyclotomic NumberField Nat
 
 variable {p : ℕ+} {k : ℕ} {K : Type u} [Field K] [CharZero K] {ζ : K} [hp : Fact (p : ℕ).Prime]
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -207,11 +207,7 @@ unity and `K` is a `p`-th cyclotomic extension of `ℚ`. -/
 @[simps]
 noncomputable def IsPrimitiveRoot.adjoinEquivRingOfIntegers' [hcycl : IsCyclotomicExtension {p} ℚ K]
     (hζ : IsPrimitiveRoot ζ p) : adjoin ℤ ({ζ} : Set K) ≃ₐ[ℤ] 𝓞 K :=
-  @adjoinEquivRingOfIntegers p 1 K _ _ _ _
-    (by
-      convert hcycl
-      rw [pow_one])
-    (by rwa [pow_one])
+  @adjoinEquivRingOfIntegers p 1 K _ _ _ _ (by convert hcycl; rw [pow_one]) (by rwa [pow_one])
 #align is_primitive_root.adjoin_equiv_ring_of_integers' IsPrimitiveRoot.adjoinEquivRingOfIntegers'
 
 /-- The ring of integers of a `p`-th cyclotomic extension of `ℚ` is a cyclotomic extension. -/
@@ -225,31 +221,19 @@ instance IsCyclotomicExtension.ring_of_integers' [IsCyclotomicExtension {p} ℚ
 cyclotomic extension of `ℚ`. -/
 noncomputable def integralPowerBasis' [hcycl : IsCyclotomicExtension {p} ℚ K]
     (hζ : IsPrimitiveRoot ζ p) : PowerBasis ℤ (𝓞 K) :=
-  @integralPowerBasis p 1 K _ _ _ _
-    (by
-      convert hcycl
-      rw [pow_one])
-    (by rwa [pow_one])
+  @integralPowerBasis p 1 K _ _ _ _ (by convert hcycl; rw [pow_one]) (by rwa [pow_one])
 #align is_primitive_root.integral_power_basis' IsPrimitiveRoot.integralPowerBasis'
 
 @[simp]
 theorem integralPowerBasis'_gen [hcycl : IsCyclotomicExtension {p} ℚ K] (hζ : IsPrimitiveRoot ζ p) :
     hζ.integralPowerBasis'.gen = ⟨ζ, hζ.IsIntegral p.Pos⟩ :=
-  @integralPowerBasis_gen p 1 K _ _ _ _
-    (by
-      convert hcycl
-      rw [pow_one])
-    (by rwa [pow_one])
+  @integralPowerBasis_gen p 1 K _ _ _ _ (by convert hcycl; rw [pow_one]) (by rwa [pow_one])
 #align is_primitive_root.integral_power_basis'_gen IsPrimitiveRoot.integralPowerBasis'_gen
 
 @[simp]
 theorem power_basis_int'_dim [hcycl : IsCyclotomicExtension {p} ℚ K] (hζ : IsPrimitiveRoot ζ p) :
     hζ.integralPowerBasis'.dim = φ p := by
-  erw [@integral_power_basis_dim p 1 K _ _ _ _
-      (by
-        convert hcycl
-        rw [pow_one])
-      (by rwa [pow_one]),
+  erw [@integral_power_basis_dim p 1 K _ _ _ _ (by convert hcycl; rw [pow_one]) (by rwa [pow_one]),
     pow_one]
 #align is_primitive_root.power_basis_int'_dim IsPrimitiveRoot.power_basis_int'_dim
 
@@ -279,11 +263,7 @@ theorem subOneIntegralPowerBasis_gen [IsCyclotomicExtension {p ^ k} ℚ K]
 extension of `ℚ`. -/
 noncomputable def subOneIntegralPowerBasis' [hcycl : IsCyclotomicExtension {p} ℚ K]
     (hζ : IsPrimitiveRoot ζ p) : PowerBasis ℤ (𝓞 K) :=
-  @subOneIntegralPowerBasis p 1 K _ _ _ _
-    (by
-      convert hcycl
-      rw [pow_one])
-    (by rwa [pow_one])
+  @subOneIntegralPowerBasis p 1 K _ _ _ _ (by convert hcycl; rw [pow_one]) (by rwa [pow_one])
 #align is_primitive_root.sub_one_integral_power_basis' IsPrimitiveRoot.subOneIntegralPowerBasis'
 
 @[simp]
@@ -291,11 +271,7 @@ theorem subOneIntegralPowerBasis'_gen [hcycl : IsCyclotomicExtension {p} ℚ K]
     (hζ : IsPrimitiveRoot ζ p) :
     hζ.subOneIntegralPowerBasis'.gen =
       ⟨ζ - 1, Subalgebra.sub_mem _ (hζ.IsIntegral p.Pos) (Subalgebra.one_mem _)⟩ :=
-  @subOneIntegralPowerBasis_gen p 1 K _ _ _ _
-    (by
-      convert hcycl
-      rw [pow_one])
-    (by rwa [pow_one])
+  @subOneIntegralPowerBasis_gen p 1 K _ _ _ _ (by convert hcycl; rw [pow_one]) (by rwa [pow_one])
 #align is_primitive_root.sub_one_integral_power_basis'_gen IsPrimitiveRoot.subOneIntegralPowerBasis'_gen
 
 end IsPrimitiveRoot

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 
 ! This file was ported from Lean 3 source module number_theory.cyclotomic.rat
-! leanprover-community/mathlib commit 2032a878972d5672e7c27c957e7a6e297b044973
+! leanprover-community/mathlib commit b353176c24d96c23f0ce1cc63efc3f55019702d9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -133,34 +133,20 @@ theorem isIntegralClosure_adjoin_singleton_of_prime [hcycl : IsCyclotomicExtensi
   exact is_integral_closure_adjoin_singleton_of_prime_pow hζ
 #align is_cyclotomic_extension.rat.is_integral_closure_adjoin_singleton_of_prime IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime
 
-attribute [-instance] CyclotomicField.algebra
-
 /-- The integral closure of `ℤ` inside `cyclotomic_field (p ^ k) ℚ` is
 `cyclotomic_ring (p ^ k) ℤ ℚ`. -/
 theorem cyclotomicRing_isIntegralClosure_of_prime_pow :
     IsIntegralClosure (CyclotomicRing (p ^ k) ℤ ℚ) ℤ (CyclotomicField (p ^ k) ℚ) :=
   by
   haveI : CharZero ℚ := StrictOrderedSemiring.to_charZero
-  have : IsCyclotomicExtension {p ^ k} ℚ (CyclotomicField (p ^ k) ℚ) :=
-    by
-    convert CyclotomicField.isCyclotomicExtension (p ^ k) _
-    · exact Subsingleton.elim _ _
-    · exact NeZero.charZero
   have hζ := zeta_spec (p ^ k) ℚ (CyclotomicField (p ^ k) ℚ)
   refine' ⟨IsFractionRing.injective _ _, fun x => ⟨fun h => ⟨⟨x, _⟩, rfl⟩, _⟩⟩
   · have := (is_integral_closure_adjoin_singleton_of_prime_pow hζ).isIntegral_iff
     obtain ⟨y, rfl⟩ := this.1 h
-    convert adjoin_mono _ y.2
-    · simp only [eq_iff_true_of_subsingleton]
-    · simp only [eq_iff_true_of_subsingleton]
-    · simp only [PNat.pow_coe, Set.singleton_subset_iff, Set.mem_setOf_eq]
-      exact hζ.pow_eq_one
-  · have : IsCyclotomicExtension {p ^ k} ℤ (CyclotomicRing (p ^ k) ℤ ℚ) :=
-      by
-      convert CyclotomicRing.isCyclotomicExtension _ ℤ ℚ
-      · exact Subsingleton.elim _ _
-      · exact NeZero.charZero
-    rintro ⟨y, rfl⟩
+    refine' adjoin_mono _ y.2
+    simp only [PNat.pow_coe, Set.singleton_subset_iff, Set.mem_setOf_eq]
+    exact hζ.pow_eq_one
+  · rintro ⟨y, rfl⟩
     exact IsIntegral.algebraMap ((IsCyclotomicExtension.integral {p ^ k} ℤ _) _)
 #align is_cyclotomic_extension.rat.cyclotomic_ring_is_integral_closure_of_prime_pow IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure_of_prime_pow
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -276,8 +276,8 @@ noncomputable def subOneIntegralPowerBasis [IsCyclotomicExtension {p ^ k} ℚ K]
       Subalgebra.sub_mem _ (hζ.IsIntegral (p ^ k).Pos) (Subalgebra.one_mem _))
     (by
       simp only [integral_power_basis_gen]
-      convert
-        Subalgebra.add_mem _ (self_mem_adjoin_singleton ℤ (⟨ζ - 1, _⟩ : 𝓞 K)) (Subalgebra.one_mem _)
+      convert Subalgebra.add_mem _ (self_mem_adjoin_singleton ℤ (⟨ζ - 1, _⟩ : 𝓞 K))
+          (Subalgebra.one_mem _)
       simp)
 #align is_primitive_root.sub_one_integral_power_basis IsPrimitiveRoot.subOneIntegralPowerBasis
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

A PR accompanying #12339.

Zulip discussion

@@ -250,9 +250,9 @@ noncomputable def subOneIntegralPowerBasis [IsCyclotomicExtension {p ^ k} ℚ K]
       convert Subalgebra.add_mem _ (self_mem_adjoin_singleton ℤ (⟨ζ - 1, _⟩ : 𝓞 K))
         (Subalgebra.one_mem _)
 -- Porting note: `simp` was able to finish the proof.
-      simp only [Subsemiring.coe_add, Subalgebra.coe_toSubsemiring,
-        OneMemClass.coe_one, sub_add_cancel]
-      exact Subalgebra.sub_mem _ (hζ.isIntegral (by simp)) (Subalgebra.one_mem _))
+      · simp only [Subsemiring.coe_add, Subalgebra.coe_toSubsemiring,
+          OneMemClass.coe_one, sub_add_cancel]
+      · exact Subalgebra.sub_mem _ (hζ.isIntegral (by simp)) (Subalgebra.one_mem _))
 #align is_primitive_root.sub_one_integral_power_basis IsPrimitiveRoot.subOneIntegralPowerBasis
 
 @[simp]

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -135,7 +135,7 @@ theorem cyclotomicRing_isIntegralClosure_of_prime_pow :
   have hζ := zeta_spec (p ^ k) ℚ (CyclotomicField (p ^ k) ℚ)
   refine ⟨IsFractionRing.injective _ _, @fun x => ⟨fun h => ⟨⟨x, ?_⟩, rfl⟩, ?_⟩⟩
 -- Porting note: having `.isIntegral_iff` inside the definition of `this` causes an error.
-  · have := (isIntegralClosure_adjoin_singleton_of_prime_pow hζ)
+  · have := isIntegralClosure_adjoin_singleton_of_prime_pow hζ
     obtain ⟨y, rfl⟩ := this.isIntegral_iff.1 h
     refine' adjoin_mono _ y.2
     simp only [PNat.pow_coe, Set.singleton_subset_iff, Set.mem_setOf_eq]
@@ -360,7 +360,7 @@ variable (K p k)
 theorem absdiscr_prime_pow [NumberField K] [IsCyclotomicExtension {p ^ k} ℚ K] :
     NumberField.discr K =
     (-1) ^ ((p ^ k : ℕ).totient / 2) * p ^ ((p : ℕ) ^ (k - 1) * ((p - 1) * k - 1)) := by
-  have hζ := (IsCyclotomicExtension.zeta_spec (p ^ k) ℚ K)
+  have hζ := IsCyclotomicExtension.zeta_spec (p ^ k) ℚ K
   let pB₁ := integralPowerBasis hζ
   apply (algebraMap ℤ ℚ).injective_int
   rw [← NumberField.discr_eq_discr _ pB₁.basis, ← Algebra.discr_localizationLocalization ℤ ℤ⁰ K]

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -372,7 +372,7 @@ theorem absdiscr_prime_pow [NumberField K] [IsCyclotomicExtension {p ^ k} ℚ K]
     congr 1
     ext i
     simp_rw [Function.comp_apply, Basis.localizationLocalization_apply, powerBasis_dim,
-      PowerBasis.coe_basis,integralPowerBasis_gen]
+      PowerBasis.coe_basis, pB₁, integralPowerBasis_gen]
     convert ← ((IsPrimitiveRoot.powerBasis ℚ hζ).basis_eq_pow i).symm using 1
   · simp_rw [algebraMap_int_eq, map_mul, map_pow, map_neg, map_one, map_natCast]
 

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -185,7 +185,7 @@ noncomputable def integralPowerBasis [IsCyclotomicExtension {p ^ k} ℚ K]
 /-- Abbreviation to see a primitive root of unity as a member of the ring of integers. -/
 abbrev toInteger {k : ℕ+} (hζ : IsPrimitiveRoot ζ k) : 𝓞 K := ⟨ζ, hζ.isIntegral k.pos⟩
 
---Porting note: the proof changed because `simp` unfolds too much.
+-- Porting note: the proof changed because `simp` unfolds too much.
 @[simp]
 theorem integralPowerBasis_gen [hcycl : IsCyclotomicExtension {p ^ k} ℚ K]
     (hζ : IsPrimitiveRoot ζ ↑(p ^ k)) :

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -133,7 +133,7 @@ theorem cyclotomicRing_isIntegralClosure_of_prime_pow :
     IsIntegralClosure (CyclotomicRing (p ^ k) ℤ ℚ) ℤ (CyclotomicField (p ^ k) ℚ) := by
   haveI : CharZero ℚ := StrictOrderedSemiring.to_charZero
   have hζ := zeta_spec (p ^ k) ℚ (CyclotomicField (p ^ k) ℚ)
-  refine' ⟨IsFractionRing.injective _ _, @fun x => ⟨fun h => ⟨⟨x, _⟩, rfl⟩, _⟩⟩
+  refine ⟨IsFractionRing.injective _ _, @fun x => ⟨fun h => ⟨⟨x, ?_⟩, rfl⟩, ?_⟩⟩
 -- Porting note: having `.isIntegral_iff` inside the definition of `this` causes an error.
   · have := (isIntegralClosure_adjoin_singleton_of_prime_pow hζ)
     obtain ⟨y, rfl⟩ := this.isIntegral_iff.1 h

We compute the absolute discriminant of cyclotomic fields.

From flt-regular.

@@ -20,6 +20,8 @@ integers of a `p ^ n`-th cyclotomic extension of `ℚ`.
   `ℤ` in `K`.
 * `IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure_of_prime_pow`: the integral
   closure of `ℤ` inside `CyclotomicField (p ^ k) ℚ` is `CyclotomicRing (p ^ k) ℤ ℚ`.
+* `IsCyclotomicExtension.Rat.absdiscr_prime_pow` and related results: the absolute discriminant
+  of cyclotomic fields.
 -/
 
 
@@ -344,4 +346,57 @@ theorem subOneIntegralPowerBasis'_gen_prime [IsCyclotomicExtension {p} ℚ K]
 
 end IsPrimitiveRoot
 
+section absdiscr
+
+namespace IsCyclotomicExtension.Rat
+
+open nonZeroDivisors IsPrimitiveRoot
+
+variable (K p k)
+
+/-- We compute the absolute discriminant of a `p ^ k`-th cyclotomic field.
+  Beware that in the cases `p ^ k = 1` and `p ^ k = 2` the formula uses `1 / 2 = 0` and `0 - 1 = 0`.
+  See also the results below. -/
+theorem absdiscr_prime_pow [NumberField K] [IsCyclotomicExtension {p ^ k} ℚ K] :
+    NumberField.discr K =
+    (-1) ^ ((p ^ k : ℕ).totient / 2) * p ^ ((p : ℕ) ^ (k - 1) * ((p - 1) * k - 1)) := by
+  have hζ := (IsCyclotomicExtension.zeta_spec (p ^ k) ℚ K)
+  let pB₁ := integralPowerBasis hζ
+  apply (algebraMap ℤ ℚ).injective_int
+  rw [← NumberField.discr_eq_discr _ pB₁.basis, ← Algebra.discr_localizationLocalization ℤ ℤ⁰ K]
+  convert IsCyclotomicExtension.discr_prime_pow hζ (cyclotomic.irreducible_rat (p ^ k).2) using 1
+  · have : pB₁.dim = (IsPrimitiveRoot.powerBasis ℚ hζ).dim := by
+      rw [← PowerBasis.finrank, ← PowerBasis.finrank]
+      exact RingOfIntegers.rank K
+    rw [← Algebra.discr_reindex _ _ (finCongr this)]
+    congr 1
+    ext i
+    simp_rw [Function.comp_apply, Basis.localizationLocalization_apply, powerBasis_dim,
+      PowerBasis.coe_basis,integralPowerBasis_gen]
+    convert ← ((IsPrimitiveRoot.powerBasis ℚ hζ).basis_eq_pow i).symm using 1
+  · simp_rw [algebraMap_int_eq, map_mul, map_pow, map_neg, map_one, map_natCast]
+
+open Nat in
+/-- We compute the absolute discriminant of a `p ^ (k + 1)`-th cyclotomic field.
+  Beware that in the case `p ^ k = 2` the formula uses `1 / 2 = 0`. See also the results below. -/
+theorem absdiscr_prime_pow_succ [NumberField K] [IsCyclotomicExtension {p ^ (k + 1)} ℚ K] :
+    NumberField.discr K =
+    (-1) ^ ((p : ℕ) ^ k * (p - 1) / 2) * p ^ ((p : ℕ) ^ k * ((p - 1) * (k + 1) - 1)) := by
+  simpa [totient_prime_pow hp.out (succ_pos k)] using absdiscr_prime_pow p (k + 1) K
+
+/-- We compute the absolute discriminant of a `p`-th cyclotomic field where `p` is prime. -/
+theorem absdiscr_prime [NumberField K] [IsCyclotomicExtension {p} ℚ K] :
+    NumberField.discr K = (-1) ^ (((p : ℕ) - 1) / 2) * p ^ ((p : ℕ) - 2) := by
+  have : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K := by
+    rw [zero_add, pow_one]
+    infer_instance
+  rw [absdiscr_prime_pow_succ p 0 K]
+  simp only [Int.reduceNeg, pow_zero, one_mul, zero_add, mul_one, mul_eq_mul_left_iff, gt_iff_lt,
+    Nat.cast_pos, PNat.pos, pow_eq_zero_iff', neg_eq_zero, one_ne_zero, ne_eq, false_and, or_false]
+  rfl
+
+end IsCyclotomicExtension.Rat
+
+end absdiscr
+
 end PowerBasis

Zulip

Initially I just wanted to add more dot notations for IsIntegral and IsAlgebraic (done in #8437); then I noticed near-duplicates Algebra.isIntegral_of_finite [Field R] [Ring A] and RingHom.IsIntegral.of_finite [CommRing R] [CommRing A] so I went on to generalize the latter to cover the former, and generalized everything in the IntegralClosure file to the noncommutative case whenever possible.

In the process I noticed more golfs, which result in this PR. Most notably, isIntegral_of_mem_of_FG is now proven using Cayley-Hamilton and doesn't depend on the Noetherian case isIntegral_of_noetherian; the latter is now proven using the former. In total the golfs makes mathlib 227 lines leaner (+487 -714).

The main changes are in the single file RingTheory/IntegralClosure:

• Change the definition of Algebra.IsIntegral which makes it unfold to IsIntegral rather than RingHom.IsIntegralElem because the former has much more APIs.

• Fix lemma names involving is_integral which are actually about IsIntegralElem: RingHom.is_integral_map → RingHom.isIntegralElem_map RingHom.is_integral_of_mem_closure → RingHom.IsIntegralElem.of_mem_closure RingHom.is_integral_zero/one → RingHom.isIntegralElem_zero/one RingHom.is_integral_add/neg/sub/mul/of_mul_unit → RingHom.IsIntegralElem.add/neg/sub/mul/of_mul_unit

• Add a lemma Algebra.IsIntegral.of_injective.

• Move isIntegral_of_(submodule_)noetherian down and golf them.

• Remove (Algebra.)isIntegral_of_finite that work only over fields, in favor of the more general (Algebra.)isIntegral.of_finite.

• Merge duplicate lemmas isIntegral_of_isScalarTower and isIntegral_tower_top_of_isIntegral into IsIntegral.tower_top.

• Golf IsIntegral.of_mem_of_fg by first proving IsIntegral.of_finite using Cayley-Hamilton.

• Add a docstring mentioning the Kurosh problem at Algebra.IsIntegral.finite. The negative solution to the problem means the theorem doesn't generalize to noncommutative algebras.

• Golf IsIntegral.tmul and isField_of_isIntegral_of_isField(').

• Combine isIntegral_trans_aux into isIntegral_trans and golf.

• Add Algebra namespace to isIntegral_sup.

• rename lemmas for dot notation: RingHom.isIntegral_trans → RingHom.IsIntegral.trans RingHom.isIntegral_quotient/tower_bot/top_of_isIntegral → RingHom.IsIntegral.quotient/tower_bot/top isIntegral_of_mem_closure' → IsIntegral.of_mem_closure' (and the '' version) isIntegral_of_surjective → Algebra.isIntegral_of_surjective

The next changed file is RingTheory/Algebraic:

• Rename: of_larger_base → tower_top (for consistency with IsIntegral) Algebra.isAlgebraic_of_finite → Algebra.IsAlgebraic.of_finite Algebra.isAlgebraic_trans → Algebra.IsAlgebraic.trans

• Add new lemmasAlgebra.IsIntegral.isAlgebraic, isAlgebraic_algHom_iff, and Algebra.IsAlgebraic.of_injective to streamline some proofs.

The generalization from CommRing to Ring requires an additional lemma scaleRoots_eval₂_mul_of_commute in Polynomial/ScaleRoots.

A lemma Algebra.lmul_injective is added to Algebra/Bilinear (in order to golf the proof of IsIntegral.of_mem_of_fg).

In all other files, I merely fix the changed names, or use newly available dot notations.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -80,7 +80,7 @@ theorem isIntegralClosure_adjoin_singleton_of_prime_pow [hcycl : IsCyclotomicExt
         (le_integralClosure_iff_isIntegral.1
           (adjoin_le_integralClosure (hζ.isIntegral (p ^ k).pos)) _)
   let B := hζ.subOnePowerBasis ℚ
-  have hint : IsIntegral ℤ B.gen := IsIntegral.sub (hζ.isIntegral (p ^ k).pos) isIntegral_one
+  have hint : IsIntegral ℤ B.gen := (hζ.isIntegral (p ^ k).pos).sub isIntegral_one
 -- Porting note: the following `haveI` was not needed because the locale `cyclotomic` set it
 -- as instances.
   letI := IsCyclotomicExtension.finiteDimensional {p ^ k} ℚ K

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

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.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

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).

leanprover/lean4#2722

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}).

leanprover/lean4#2783

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:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[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>

@@ -31,8 +31,6 @@ open scoped Cyclotomic NumberField Nat
 
 variable {p : ℕ+} {k : ℕ} {K : Type u} [Field K] [CharZero K] {ζ : K} [hp : Fact (p : ℕ).Prime]
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 namespace IsCyclotomicExtension.Rat
 
 /-- The discriminant of the power basis given by `ζ - 1`. -/
@@ -92,7 +90,7 @@ theorem isIntegralClosure_adjoin_singleton_of_prime_pow [hcycl : IsCyclotomicExt
   replace H := Subalgebra.smul_mem _ H u.inv
 -- Porting note: the proof is slightly different because of coercions.
   rw [← smul_assoc, ← smul_mul_assoc, Units.inv_eq_val_inv, zsmul_eq_mul, ← Int.cast_mul,
-    Units.inv_mul, Int.cast_one, one_mul, PNat.pow_coe, Nat.cast_pow, smul_def, map_pow] at H
+    Units.inv_mul, Int.cast_one, one_mul, smul_def, map_pow] at H
   cases k
   · haveI : IsCyclotomicExtension {1} ℚ K := by simpa using hcycl
     have : x ∈ (⊥ : Subalgebra ℚ K) := by
@@ -303,7 +301,7 @@ theorem zeta_sub_one_prime_of_two_pow [IsCyclotomicExtension {(2 : ℕ+) ^ (k +
     Prime (hζ.toInteger - 1) := by
   letI := IsCyclotomicExtension.numberField {(2 : ℕ+) ^ (k + 1)} ℚ K
   refine Ideal.prime_of_irreducible_absNorm_span (fun h ↦ ?_) ?_
-  · apply hζ.pow_ne_one_of_pos_of_lt zero_lt_one (one_lt_pow (by norm_num) (by simp))
+  · apply hζ.pow_ne_one_of_pos_of_lt zero_lt_one (one_lt_pow (by decide) (by simp))
     rw [← Subalgebra.coe_eq_zero] at h
     simpa [sub_eq_zero] using h
   rw [Nat.irreducible_iff_prime, Ideal.absNorm_span_singleton, ← Nat.prime_iff,

This PR tests a string-based tool for renaming declarations.

Inspired by this Zulip thread, I am trying to reduce the diff of #8406.

This PR makes the following renames:

| From | To |

@@ -82,7 +82,7 @@ theorem isIntegralClosure_adjoin_singleton_of_prime_pow [hcycl : IsCyclotomicExt
         (le_integralClosure_iff_isIntegral.1
           (adjoin_le_integralClosure (hζ.isIntegral (p ^ k).pos)) _)
   let B := hζ.subOnePowerBasis ℚ
-  have hint : IsIntegral ℤ B.gen := isIntegral_sub (hζ.isIntegral (p ^ k).pos) isIntegral_one
+  have hint : IsIntegral ℤ B.gen := IsIntegral.sub (hζ.isIntegral (p ^ k).pos) isIntegral_one
 -- Porting note: the following `haveI` was not needed because the locale `cyclotomic` set it
 -- as instances.
   letI := IsCyclotomicExtension.finiteDimensional {p ^ k} ℚ K

We add zeta_sub_one_prime: in a p^(k+1)-th cyclotomic extension ζ-1 is prime.

@@ -5,6 +5,7 @@ Authors: Riccardo Brasca
 -/
 import Mathlib.NumberTheory.Cyclotomic.Discriminant
 import Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral
+import Mathlib.RingTheory.Ideal.Norm
 
 #align_import number_theory.cyclotomic.rat from "leanprover-community/mathlib"@"b353176c24d96c23f0ce1cc63efc3f55019702d9"
 
@@ -181,11 +182,14 @@ noncomputable def integralPowerBasis [IsCyclotomicExtension {p ^ k} ℚ K]
   (Algebra.adjoin.powerBasis' (hζ.isIntegral (p ^ k).pos)).map hζ.adjoinEquivRingOfIntegers
 #align is_primitive_root.integral_power_basis IsPrimitiveRoot.integralPowerBasis
 
+/-- Abbreviation to see a primitive root of unity as a member of the ring of integers. -/
+abbrev toInteger {k : ℕ+} (hζ : IsPrimitiveRoot ζ k) : 𝓞 K := ⟨ζ, hζ.isIntegral k.pos⟩
+
 --Porting note: the proof changed because `simp` unfolds too much.
 @[simp]
 theorem integralPowerBasis_gen [hcycl : IsCyclotomicExtension {p ^ k} ℚ K]
     (hζ : IsPrimitiveRoot ζ ↑(p ^ k)) :
-    hζ.integralPowerBasis.gen = ⟨ζ, hζ.isIntegral (p ^ k).pos⟩ :=
+    hζ.integralPowerBasis.gen = hζ.toInteger :=
   Subtype.ext <| show algebraMap _ K hζ.integralPowerBasis.gen = _ by
     rw [integralPowerBasis, PowerBasis.map_gen, adjoin.powerBasis'_gen]
     simp only [adjoinEquivRingOfIntegers_apply, IsIntegralClosure.algebraMap_lift]
@@ -223,7 +227,7 @@ noncomputable def integralPowerBasis' [hcycl : IsCyclotomicExtension {p} ℚ K]
 
 @[simp]
 theorem integralPowerBasis'_gen [hcycl : IsCyclotomicExtension {p} ℚ K] (hζ : IsPrimitiveRoot ζ p) :
-    hζ.integralPowerBasis'.gen = ⟨ζ, hζ.isIntegral p.pos⟩ :=
+    hζ.integralPowerBasis'.gen = hζ.toInteger :=
   @integralPowerBasis_gen p 1 K _ _ _ _ (by convert hcycl; rw [pow_one]) (by rwa [pow_one])
 #align is_primitive_root.integral_power_basis'_gen IsPrimitiveRoot.integralPowerBasis'_gen
 
@@ -242,7 +246,7 @@ noncomputable def subOneIntegralPowerBasis [IsCyclotomicExtension {p ^ k} ℚ K]
     (isIntegral_of_mem_ringOfIntegers <|
       Subalgebra.sub_mem _ (hζ.isIntegral (p ^ k).pos) (Subalgebra.one_mem _))
     (by
-      simp only [integralPowerBasis_gen]
+      simp only [integralPowerBasis_gen, toInteger]
       convert Subalgebra.add_mem _ (self_mem_adjoin_singleton ℤ (⟨ζ - 1, _⟩ : 𝓞 K))
         (Subalgebra.one_mem _)
 -- Porting note: `simp` was able to finish the proof.
@@ -269,11 +273,77 @@ noncomputable def subOneIntegralPowerBasis' [hcycl : IsCyclotomicExtension {p} 
 @[simp]
 theorem subOneIntegralPowerBasis'_gen [hcycl : IsCyclotomicExtension {p} ℚ K]
     (hζ : IsPrimitiveRoot ζ p) :
-    hζ.subOneIntegralPowerBasis'.gen =
-      ⟨ζ - 1, Subalgebra.sub_mem _ (hζ.isIntegral p.pos) (Subalgebra.one_mem _)⟩ :=
+    hζ.subOneIntegralPowerBasis'.gen = hζ.toInteger - 1 :=
   @subOneIntegralPowerBasis_gen p 1 K _ _ _ _ (by convert hcycl; rw [pow_one]) (by rwa [pow_one])
 #align is_primitive_root.sub_one_integral_power_basis'_gen IsPrimitiveRoot.subOneIntegralPowerBasis'_gen
 
+/-- `ζ - 1` is prime if `p ≠ 2` and `ζ` is a primitive `p ^ (k + 1)`-th root of unity.
+  See `zeta_sub_one_prime` for a general statement. -/
+theorem zeta_sub_one_prime_of_ne_two [IsCyclotomicExtension {p ^ (k + 1)} ℚ K]
+    (hζ : IsPrimitiveRoot ζ ↑(p ^ (k + 1))) (hodd : p ≠ 2) :
+    Prime (hζ.toInteger - 1) := by
+  letI := IsCyclotomicExtension.numberField {p ^ (k + 1)} ℚ K
+  refine Ideal.prime_of_irreducible_absNorm_span (fun h ↦ ?_) ?_
+  · apply hζ.pow_ne_one_of_pos_of_lt zero_lt_one (one_lt_pow hp.out.one_lt (by simp))
+    rw [← Subalgebra.coe_eq_zero] at h
+    simpa [sub_eq_zero] using h
+  rw [Nat.irreducible_iff_prime, Ideal.absNorm_span_singleton, ← Nat.prime_iff,
+    ← Int.prime_iff_natAbs_prime]
+  convert Nat.prime_iff_prime_int.1 hp.out
+  apply RingHom.injective_int (algebraMap ℤ ℚ)
+  rw [← Algebra.norm_localization (Sₘ := K) ℤ (nonZeroDivisors ℤ), Subalgebra.algebraMap_eq]
+  simp only [PNat.pow_coe, id.map_eq_id, RingHomCompTriple.comp_eq, RingHom.coe_coe,
+    Subalgebra.coe_val, algebraMap_int_eq, map_natCast]
+  exact hζ.sub_one_norm_prime_ne_two (Polynomial.cyclotomic.irreducible_rat (PNat.pos _)) hodd
+
+/-- `ζ - 1` is prime if `ζ` is a primitive `2 ^ (k + 1)`-th root of unity.
+  See `zeta_sub_one_prime` for a general statement. -/
+theorem zeta_sub_one_prime_of_two_pow [IsCyclotomicExtension {(2 : ℕ+) ^ (k + 1)} ℚ K]
+    (hζ : IsPrimitiveRoot ζ ↑((2 : ℕ+) ^ (k + 1))) :
+    Prime (hζ.toInteger - 1) := by
+  letI := IsCyclotomicExtension.numberField {(2 : ℕ+) ^ (k + 1)} ℚ K
+  refine Ideal.prime_of_irreducible_absNorm_span (fun h ↦ ?_) ?_
+  · apply hζ.pow_ne_one_of_pos_of_lt zero_lt_one (one_lt_pow (by norm_num) (by simp))
+    rw [← Subalgebra.coe_eq_zero] at h
+    simpa [sub_eq_zero] using h
+  rw [Nat.irreducible_iff_prime, Ideal.absNorm_span_singleton, ← Nat.prime_iff,
+    ← Int.prime_iff_natAbs_prime]
+  cases k
+  · convert Prime.neg Int.prime_two
+    apply RingHom.injective_int (algebraMap ℤ ℚ)
+    rw [← Algebra.norm_localization (Sₘ := K) ℤ (nonZeroDivisors ℤ), Subalgebra.algebraMap_eq]
+    simp only [Nat.zero_eq, PNat.pow_coe, id.map_eq_id, RingHomCompTriple.comp_eq, RingHom.coe_coe,
+      Subalgebra.coe_val, algebraMap_int_eq, map_neg, map_ofNat]
+    simpa using hζ.pow_sub_one_norm_two (cyclotomic.irreducible_rat (by simp))
+  convert Int.prime_two
+  apply RingHom.injective_int (algebraMap ℤ ℚ)
+  rw [← Algebra.norm_localization (Sₘ := K) ℤ (nonZeroDivisors ℤ), Subalgebra.algebraMap_eq]
+  simp only [PNat.pow_coe, id.map_eq_id, RingHomCompTriple.comp_eq, RingHom.coe_coe,
+    Subalgebra.coe_val, algebraMap_int_eq, map_natCast]
+  exact hζ.sub_one_norm_two Nat.AtLeastTwo.prop (cyclotomic.irreducible_rat (by simp))
+
+/-- `ζ - 1` is prime if `ζ` is a primitive `p ^ (k + 1)`-th root of unity. -/
+theorem zeta_sub_one_prime [IsCyclotomicExtension {p ^ (k + 1)} ℚ K]
+    (hζ : IsPrimitiveRoot ζ ↑(p ^ (k + 1))) : Prime (hζ.toInteger - 1) := by
+  by_cases htwo : p = 2
+  · subst htwo
+    apply hζ.zeta_sub_one_prime_of_two_pow
+  · apply hζ.zeta_sub_one_prime_of_ne_two htwo
+
+/-- `ζ - 1` is prime if `ζ` is a primitive `p`-th root of unity. -/
+theorem zeta_sub_one_prime' [h : IsCyclotomicExtension {p} ℚ K] (hζ : IsPrimitiveRoot ζ p) :
+    Prime ((hζ.toInteger - 1)) := by
+  convert zeta_sub_one_prime (k := 0) (by simpa)
+  simpa
+
+theorem subOneIntegralPowerBasis_gen_prime [IsCyclotomicExtension {p ^ (k + 1)} ℚ K]
+    (hζ : IsPrimitiveRoot ζ ↑(p ^ (k + 1))) :
+    Prime hζ.subOneIntegralPowerBasis.gen := by simpa using hζ.zeta_sub_one_prime
+
+theorem subOneIntegralPowerBasis'_gen_prime [IsCyclotomicExtension {p} ℚ K]
+    (hζ : IsPrimitiveRoot ζ ↑p) :
+    Prime hζ.subOneIntegralPowerBasis'.gen := by simpa using hζ.zeta_sub_one_prime'
+
 end IsPrimitiveRoot
 
 end PowerBasis

@@ -30,7 +30,7 @@ open scoped Cyclotomic NumberField Nat
 
 variable {p : ℕ+} {k : ℕ} {K : Type u} [Field K] [CharZero K] {ζ : K} [hp : Fact (p : ℕ).Prime]
 
-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 IsCyclotomicExtension.Rat
 

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
-
-! This file was ported from Lean 3 source module number_theory.cyclotomic.rat
-! leanprover-community/mathlib commit b353176c24d96c23f0ce1cc63efc3f55019702d9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.NumberTheory.Cyclotomic.Discriminant
 import Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral
 
+#align_import number_theory.cyclotomic.rat from "leanprover-community/mathlib"@"b353176c24d96c23f0ce1cc63efc3f55019702d9"
+
 /-!
 # Ring of integers of `p ^ n`-th cyclotomic fields
 We gather results about cyclotomic extensions of `ℚ`. In particular, we compute the ring of

@@ -114,10 +114,10 @@ theorem isIntegralClosure_adjoin_singleton_of_prime_pow [hcycl : IsCyclotomicExt
       haveI : CharZero ℚ := StrictOrderedSemiring.to_charZero
       rw [IsPrimitiveRoot.subOnePowerBasis_gen,
         map_injective (algebraMap ℤ ℚ) (algebraMap ℤ ℚ).injective_int h₂]
-      exact cyclotomic_prime_pow_comp_x_add_one_isEisensteinAt p _
+      exact cyclotomic_prime_pow_comp_X_add_one_isEisensteinAt p _
     refine'
       adjoin_le _
-        (mem_adjoin_of_smul_prime_pow_smul_of_minpoly_is_eiseinstein_at (n := n)
+        (mem_adjoin_of_smul_prime_pow_smul_of_minpoly_isEisensteinAt (n := n)
           (Nat.prime_iff_prime_int.1 hp.out) hint h (by simpa using H) hmin)
     simp only [Set.singleton_subset_iff, SetLike.mem_coe]
     exact Subalgebra.sub_mem _ (self_mem_adjoin_singleton ℤ _) (Subalgebra.one_mem _)