ring_theory.polynomial.cyclotomic.roots ⟷ Mathlib.RingTheory.Polynomial.Cyclotomic.Roots

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

@@ -49,7 +49,7 @@ theorem isRoot_of_unity_of_root_cyclotomic {ζ : R} {i : ℕ} (hi : i ∈ n.divi
   rcases n.eq_zero_or_pos with (rfl | hn)
   · exact pow_zero _
   have := congr_arg (eval ζ) (prod_cyclotomic_eq_X_pow_sub_one hn R).symm
-  rw [eval_sub, eval_pow, eval_X, eval_one] at this 
+  rw [eval_sub, eval_pow, eval_X, eval_one] at this
   convert eq_add_of_sub_eq' this
   convert (add_zero _).symm
   apply eval_eq_zero_of_dvd_of_eval_eq_zero _ h
@@ -77,7 +77,7 @@ theorem IsPrimitiveRoot.isRoot_cyclotomic (hpos : 0 < n) {μ : R} (h : IsPrimiti
   by
   rw [← mem_roots (cyclotomic_ne_zero n R), cyclotomic_eq_prod_X_sub_primitive_roots h,
     roots_prod_X_sub_C, ← Finset.mem_def]
-  rwa [← mem_primitiveRoots hpos] at h 
+  rwa [← mem_primitiveRoots hpos] at h
 #align is_primitive_root.is_root_cyclotomic IsPrimitiveRoot.isRoot_cyclotomic
 -/
 
@@ -97,21 +97,21 @@ private theorem is_root_cyclotomic_iff' {n : ℕ} {K : Type _} [Field K] {μ : K
     rw [isOfFinOrder_iff_pow_eq_one]
     exact ⟨n, hnpos, hμn⟩
   have := pow_orderOf_eq_one μ
-  rw [isRoot_of_unity_iff ho] at this 
+  rw [isRoot_of_unity_iff ho] at this
   obtain ⟨i, hio, hiμ⟩ := this
   replace hio := Nat.dvd_of_mem_divisors hio
-  rw [IsPrimitiveRoot.not_iff] at hnμ 
-  rw [← orderOf_dvd_iff_pow_eq_one] at hμn 
+  rw [IsPrimitiveRoot.not_iff] at hnμ
+  rw [← orderOf_dvd_iff_pow_eq_one] at hμn
   have key : i < n := (Nat.le_of_dvd ho hio).trans_lt ((Nat.le_of_dvd hnpos hμn).lt_of_ne hnμ)
   have key' : i ∣ n := hio.trans hμn
-  rw [← Polynomial.dvd_iff_isRoot] at hμ hiμ 
+  rw [← Polynomial.dvd_iff_isRoot] at hμ hiμ
   have hni : {i, n} ⊆ n.divisors := by simpa [Finset.insert_subset_iff, key'] using hnpos.ne'
   obtain ⟨k, hk⟩ := hiμ
   obtain ⟨j, hj⟩ := hμ
   have := prod_cyclotomic_eq_X_pow_sub_one hnpos K
-  rw [← Finset.prod_sdiff hni, Finset.prod_pair key.ne, hk, hj] at this 
+  rw [← Finset.prod_sdiff hni, Finset.prod_pair key.ne, hk, hj] at this
   have hn := (X_pow_sub_one_separable_iff.mpr <| NeZero.natCast_ne n K).Squarefree
-  rw [← this, Squarefree] at hn 
+  rw [← this, Squarefree] at hn
   contrapose! hn
   refine' ⟨X - C μ, ⟨(∏ x in n.divisors \ {i, n}, cyclotomic x K) * k * j, by ring⟩, _⟩
   simp [Polynomial.isUnit_iff_degree_eq_zero]
@@ -133,7 +133,7 @@ theorem roots_cyclotomic_nodup [NeZero (n : R)] : (cyclotomic n R).roots.Nodup :
   by
   obtain h | ⟨ζ, hζ⟩ := (cyclotomic n R).roots.empty_or_exists_mem
   · exact h.symm ▸ Multiset.nodup_zero
-  rw [mem_roots <| cyclotomic_ne_zero n R, is_root_cyclotomic_iff] at hζ 
+  rw [mem_roots <| cyclotomic_ne_zero n R, is_root_cyclotomic_iff] at hζ
   refine'
     Multiset.nodup_of_le
       (roots.le_of_dvd (X_pow_sub_C_ne_zero (NeZero.pos_of_neZero_natCast R) 1) <|
@@ -174,25 +174,25 @@ end IsDomain
 theorem cyclotomic_injective [CharZero R] : Function.Injective fun n => cyclotomic n R :=
   by
   intro n m hnm
-  simp only at hnm 
+  simp only at hnm
   rcases eq_or_ne n 0 with (rfl | hzero)
-  · rw [cyclotomic_zero] at hnm 
+  · rw [cyclotomic_zero] at hnm
     replace hnm := congr_arg nat_degree hnm
-    rw [nat_degree_one, nat_degree_cyclotomic] at hnm 
+    rw [nat_degree_one, nat_degree_cyclotomic] at hnm
     by_contra
     exact (Nat.totient_pos (zero_lt_iff.2 (Ne.symm h))).Ne hnm
   · haveI := NeZero.mk hzero
-    rw [← map_cyclotomic_int _ R, ← map_cyclotomic_int _ R] at hnm 
+    rw [← map_cyclotomic_int _ R, ← map_cyclotomic_int _ R] at hnm
     replace hnm := map_injective (Int.castRingHom R) Int.cast_injective hnm
     replace hnm := congr_arg (map (Int.castRingHom ℂ)) hnm
-    rw [map_cyclotomic_int, map_cyclotomic_int] at hnm 
+    rw [map_cyclotomic_int, map_cyclotomic_int] at hnm
     have hprim := Complex.isPrimitiveRoot_exp _ hzero
     have hroot := is_root_cyclotomic_iff.2 hprim
-    rw [hnm] at hroot 
+    rw [hnm] at hroot
     haveI hmzero : NeZero m := ⟨fun h => by simpa [h] using hroot⟩
-    rw [is_root_cyclotomic_iff] at hroot 
+    rw [is_root_cyclotomic_iff] at hroot
     replace hprim := hprim.eq_order_of
-    rwa [← IsPrimitiveRoot.eq_orderOf hroot] at hprim 
+    rwa [← IsPrimitiveRoot.eq_orderOf hroot] at hprim
 #align polynomial.cyclotomic_injective Polynomial.cyclotomic_injective
 -/
 

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

@@ -93,7 +93,7 @@ private theorem is_root_cyclotomic_iff' {n : ℕ} {K : Type _} [Field K] {μ : K
     all_goals infer_instance
   by_contra hnμ
   have ho : 0 < orderOf μ := by
-    apply orderOf_pos'
+    apply IsOfFinOrder.orderOf_pos
     rw [isOfFinOrder_iff_pow_eq_one]
     exact ⟨n, hnpos, hμn⟩
   have := pow_orderOf_eq_one μ

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 -/
-import Mathbin.RingTheory.Polynomial.Cyclotomic.Basic
-import Mathbin.RingTheory.RootsOfUnity.Minpoly
+import RingTheory.Polynomial.Cyclotomic.Basic
+import RingTheory.RootsOfUnity.Minpoly
 
 #align_import ring_theory.polynomial.cyclotomic.roots from "leanprover-community/mathlib"@"2a0ce625dbb0ffbc7d1316597de0b25c1ec75303"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 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 ring_theory.polynomial.cyclotomic.roots
-! leanprover-community/mathlib commit 2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Polynomial.Cyclotomic.Basic
 import Mathbin.RingTheory.RootsOfUnity.Minpoly
 
+#align_import ring_theory.polynomial.cyclotomic.roots from "leanprover-community/mathlib"@"2a0ce625dbb0ffbc7d1316597de0b25c1ec75303"
+
 /-!
 # Roots of cyclotomic polynomials.
 

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

@@ -108,7 +108,7 @@ private theorem is_root_cyclotomic_iff' {n : ℕ} {K : Type _} [Field K] {μ : K
   have key : i < n := (Nat.le_of_dvd ho hio).trans_lt ((Nat.le_of_dvd hnpos hμn).lt_of_ne hnμ)
   have key' : i ∣ n := hio.trans hμn
   rw [← Polynomial.dvd_iff_isRoot] at hμ hiμ 
-  have hni : {i, n} ⊆ n.divisors := by simpa [Finset.insert_subset, key'] using hnpos.ne'
+  have hni : {i, n} ⊆ n.divisors := by simpa [Finset.insert_subset_iff, key'] using hnpos.ne'
   obtain ⟨k, hk⟩ := hiμ
   obtain ⟨j, hj⟩ := hμ
   have := prod_cyclotomic_eq_X_pow_sub_one hnpos K

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

@@ -45,6 +45,7 @@ namespace Polynomial
 
 variable {R : Type _} [CommRing R] {n : ℕ}
 
+#print Polynomial.isRoot_of_unity_of_root_cyclotomic /-
 theorem isRoot_of_unity_of_root_cyclotomic {ζ : R} {i : ℕ} (hi : i ∈ n.divisors)
     (h : (cyclotomic i R).IsRoot ζ) : ζ ^ n = 1 :=
   by
@@ -57,18 +58,22 @@ theorem isRoot_of_unity_of_root_cyclotomic {ζ : R} {i : ℕ} (hi : i ∈ n.divi
   apply eval_eq_zero_of_dvd_of_eval_eq_zero _ h
   exact Finset.dvd_prod_of_mem _ hi
 #align polynomial.is_root_of_unity_of_root_cyclotomic Polynomial.isRoot_of_unity_of_root_cyclotomic
+-/
 
 section IsDomain
 
 variable [IsDomain R]
 
+#print isRoot_of_unity_iff /-
 theorem isRoot_of_unity_iff (h : 0 < n) (R : Type _) [CommRing R] [IsDomain R] {ζ : R} :
     ζ ^ n = 1 ↔ ∃ i ∈ n.divisors, (cyclotomic i R).IsRoot ζ := by
   rw [← mem_nth_roots h, nth_roots, mem_roots <| X_pow_sub_C_ne_zero h _, C_1, ←
       prod_cyclotomic_eq_X_pow_sub_one h, is_root_prod] <;>
     infer_instance
 #align is_root_of_unity_iff isRoot_of_unity_iff
+-/
 
+#print IsPrimitiveRoot.isRoot_cyclotomic /-
 /-- Any `n`-th primitive root of unity is a root of `cyclotomic n R`.-/
 theorem IsPrimitiveRoot.isRoot_cyclotomic (hpos : 0 < n) {μ : R} (h : IsPrimitiveRoot μ n) :
     IsRoot (cyclotomic n R) μ :=
@@ -77,6 +82,7 @@ theorem IsPrimitiveRoot.isRoot_cyclotomic (hpos : 0 < n) {μ : R} (h : IsPrimiti
     roots_prod_X_sub_C, ← Finset.mem_def]
   rwa [← mem_primitiveRoots hpos] at h 
 #align is_primitive_root.is_root_cyclotomic IsPrimitiveRoot.isRoot_cyclotomic
+-/
 
 private theorem is_root_cyclotomic_iff' {n : ℕ} {K : Type _} [Field K] {μ : K} [NeZero (n : K)] :
     IsRoot (cyclotomic n K) μ ↔ IsPrimitiveRoot μ n :=
@@ -114,6 +120,7 @@ private theorem is_root_cyclotomic_iff' {n : ℕ} {K : Type _} [Field K] {μ : K
   simp [Polynomial.isUnit_iff_degree_eq_zero]
   all_goals infer_instance
 
+#print Polynomial.isRoot_cyclotomic_iff /-
 theorem isRoot_cyclotomic_iff [NeZero (n : R)] {μ : R} :
     IsRoot (cyclotomic n R) μ ↔ IsPrimitiveRoot μ n :=
   by
@@ -122,7 +129,9 @@ theorem isRoot_cyclotomic_iff [NeZero (n : R)] {μ : R} :
   rw [← is_root_map_iff hf, ← IsPrimitiveRoot.map_iff_of_injective hf, map_cyclotomic, ←
     is_root_cyclotomic_iff']
 #align polynomial.is_root_cyclotomic_iff Polynomial.isRoot_cyclotomic_iff
+-/
 
+#print Polynomial.roots_cyclotomic_nodup /-
 theorem roots_cyclotomic_nodup [NeZero (n : R)] : (cyclotomic n R).roots.Nodup :=
   by
   obtain h | ⟨ζ, hζ⟩ := (cyclotomic n R).roots.empty_or_exists_mem
@@ -134,18 +143,24 @@ theorem roots_cyclotomic_nodup [NeZero (n : R)] : (cyclotomic n R).roots.Nodup :
         cyclotomic.dvd_X_pow_sub_one n R)
       hζ.nth_roots_nodup
 #align polynomial.roots_cyclotomic_nodup Polynomial.roots_cyclotomic_nodup
+-/
 
+#print Polynomial.cyclotomic.roots_to_finset_eq_primitiveRoots /-
 theorem cyclotomic.roots_to_finset_eq_primitiveRoots [NeZero (n : R)] :
     (⟨(cyclotomic n R).roots, roots_cyclotomic_nodup⟩ : Finset _) = primitiveRoots n R := by ext;
   simp [cyclotomic_ne_zero n R, is_root_cyclotomic_iff, mem_primitiveRoots,
     NeZero.pos_of_neZero_natCast R]
 #align polynomial.cyclotomic.roots_to_finset_eq_primitive_roots Polynomial.cyclotomic.roots_to_finset_eq_primitiveRoots
+-/
 
+#print Polynomial.cyclotomic.roots_eq_primitiveRoots_val /-
 theorem cyclotomic.roots_eq_primitiveRoots_val [NeZero (n : R)] :
     (cyclotomic n R).roots = (primitiveRoots n R).val := by
   rw [← cyclotomic.roots_to_finset_eq_primitive_roots]
 #align polynomial.cyclotomic.roots_eq_primitive_roots_val Polynomial.cyclotomic.roots_eq_primitiveRoots_val
+-/
 
+#print Polynomial.isRoot_cyclotomic_iff_charZero /-
 /-- If `R` is of characteristic zero, then `ζ` is a root of `cyclotomic n R` if and only if it is a
 primitive `n`-th root of unity. -/
 theorem isRoot_cyclotomic_iff_charZero {n : ℕ} {R : Type _} [CommRing R] [IsDomain R] [CharZero R]
@@ -153,9 +168,11 @@ theorem isRoot_cyclotomic_iff_charZero {n : ℕ} {R : Type _} [CommRing R] [IsDo
   letI := NeZero.of_gt hn
   is_root_cyclotomic_iff
 #align polynomial.is_root_cyclotomic_iff_char_zero Polynomial.isRoot_cyclotomic_iff_charZero
+-/
 
 end IsDomain
 
+#print Polynomial.cyclotomic_injective /-
 /-- Over a ring `R` of characteristic zero, `λ n, cyclotomic n R` is injective. -/
 theorem cyclotomic_injective [CharZero R] : Function.Injective fun n => cyclotomic n R :=
   by
@@ -180,7 +197,9 @@ theorem cyclotomic_injective [CharZero R] : Function.Injective fun n => cyclotom
     replace hprim := hprim.eq_order_of
     rwa [← IsPrimitiveRoot.eq_orderOf hroot] at hprim 
 #align polynomial.cyclotomic_injective Polynomial.cyclotomic_injective
+-/
 
+#print IsPrimitiveRoot.minpoly_dvd_cyclotomic /-
 /-- The minimal polynomial of a primitive `n`-th root of unity `μ` divides `cyclotomic n ℤ`. -/
 theorem IsPrimitiveRoot.minpoly_dvd_cyclotomic {n : ℕ} {K : Type _} [Field K] {μ : K}
     (h : IsPrimitiveRoot μ n) (hpos : 0 < n) [CharZero K] : minpoly ℤ μ ∣ cyclotomic n ℤ :=
@@ -188,11 +207,13 @@ theorem IsPrimitiveRoot.minpoly_dvd_cyclotomic {n : ℕ} {K : Type _} [Field K]
   apply minpoly.isIntegrallyClosed_dvd (h.is_integral hpos)
   simpa [aeval_def, eval₂_eq_eval_map, is_root.def] using h.is_root_cyclotomic hpos
 #align is_primitive_root.minpoly_dvd_cyclotomic IsPrimitiveRoot.minpoly_dvd_cyclotomic
+-/
 
 section minpoly
 
 open IsPrimitiveRoot Complex
 
+#print IsPrimitiveRoot.minpoly_eq_cyclotomic_of_irreducible /-
 theorem IsPrimitiveRoot.minpoly_eq_cyclotomic_of_irreducible {K : Type _} [Field K] {R : Type _}
     [CommRing R] [IsDomain R] {μ : R} {n : ℕ} [Algebra K R] (hμ : IsPrimitiveRoot μ n)
     (h : Irreducible <| cyclotomic n K) [NeZero (n : K)] : cyclotomic n K = minpoly K μ :=
@@ -201,7 +222,9 @@ theorem IsPrimitiveRoot.minpoly_eq_cyclotomic_of_irreducible {K : Type _} [Field
   refine' minpoly.eq_of_irreducible_of_monic h _ (cyclotomic.monic n K)
   rwa [aeval_def, eval₂_eq_eval_map, map_cyclotomic, ← is_root.def, is_root_cyclotomic_iff]
 #align is_primitive_root.minpoly_eq_cyclotomic_of_irreducible IsPrimitiveRoot.minpoly_eq_cyclotomic_of_irreducible
+-/
 
+#print Polynomial.cyclotomic_eq_minpoly /-
 /-- `cyclotomic n ℤ` is the minimal polynomial of a primitive `n`-th root of unity `μ`. -/
 theorem cyclotomic_eq_minpoly {n : ℕ} {K : Type _} [Field K] {μ : K} (h : IsPrimitiveRoot μ n)
     (hpos : 0 < n) [CharZero K] : cyclotomic n ℤ = minpoly ℤ μ :=
@@ -211,7 +234,9 @@ theorem cyclotomic_eq_minpoly {n : ℕ} {K : Type _} [Field K] {μ : K} (h : IsP
       (h.minpoly_dvd_cyclotomic hpos) _
   simpa [nat_degree_cyclotomic n ℤ] using totient_le_degree_minpoly h
 #align polynomial.cyclotomic_eq_minpoly Polynomial.cyclotomic_eq_minpoly
+-/
 
+#print Polynomial.cyclotomic_eq_minpoly_rat /-
 /-- `cyclotomic n ℚ` is the minimal polynomial of a primitive `n`-th root of unity `μ`. -/
 theorem cyclotomic_eq_minpoly_rat {n : ℕ} {K : Type _} [Field K] {μ : K} (h : IsPrimitiveRoot μ n)
     (hpos : 0 < n) [CharZero K] : cyclotomic n ℚ = minpoly ℚ μ :=
@@ -219,7 +244,9 @@ theorem cyclotomic_eq_minpoly_rat {n : ℕ} {K : Type _} [Field K] {μ : K} (h :
   rw [← map_cyclotomic_int, cyclotomic_eq_minpoly h hpos]
   exact (minpoly.isIntegrallyClosed_eq_field_fractions' _ (IsIntegral h hpos)).symm
 #align polynomial.cyclotomic_eq_minpoly_rat Polynomial.cyclotomic_eq_minpoly_rat
+-/
 
+#print Polynomial.cyclotomic.irreducible /-
 /-- `cyclotomic n ℤ` is irreducible. -/
 theorem cyclotomic.irreducible {n : ℕ} (hpos : 0 < n) : Irreducible (cyclotomic n ℤ) :=
   by
@@ -227,7 +254,9 @@ theorem cyclotomic.irreducible {n : ℕ} (hpos : 0 < n) : Irreducible (cyclotomi
   apply minpoly.irreducible
   exact (is_primitive_root_exp n hpos.ne').IsIntegral hpos
 #align polynomial.cyclotomic.irreducible Polynomial.cyclotomic.irreducible
+-/
 
+#print Polynomial.cyclotomic.irreducible_rat /-
 /-- `cyclotomic n ℚ` is irreducible. -/
 theorem cyclotomic.irreducible_rat {n : ℕ} (hpos : 0 < n) : Irreducible (cyclotomic n ℚ) :=
   by
@@ -236,7 +265,9 @@ theorem cyclotomic.irreducible_rat {n : ℕ} (hpos : 0 < n) : Irreducible (cyclo
     (is_primitive.irreducible_iff_irreducible_map_fraction_map (cyclotomic.is_primitive n ℤ)).1
       (cyclotomic.irreducible hpos)
 #align polynomial.cyclotomic.irreducible_rat Polynomial.cyclotomic.irreducible_rat
+-/
 
+#print Polynomial.cyclotomic.isCoprime_rat /-
 /-- If `n ≠ m`, then `(cyclotomic n ℚ)` and `(cyclotomic m ℚ)` are coprime. -/
 theorem cyclotomic.isCoprime_rat {n m : ℕ} (h : n ≠ m) :
     IsCoprime (cyclotomic n ℚ) (cyclotomic m ℚ) :=
@@ -253,6 +284,7 @@ theorem cyclotomic.isCoprime_rat {n m : ℕ} (h : n ≠ m) :
           Irreducible.associated_of_dvd (cyclotomic.irreducible_rat hnzero)
             (cyclotomic.irreducible_rat hmzero) hdiv
 #align polynomial.cyclotomic.is_coprime_rat Polynomial.cyclotomic.isCoprime_rat
+-/
 
 end minpoly
 

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

@@ -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 ring_theory.polynomial.cyclotomic.roots
-! leanprover-community/mathlib commit 7fdeecc0d03cd40f7a165e6cf00a4d2286db599f
+! leanprover-community/mathlib commit 2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.RootsOfUnity.Minpoly
 /-!
 # Roots of cyclotomic polynomials.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We gather results about roots of cyclotomic polynomials. In particular we show in
 `polynomial.cyclotomic_eq_minpoly` that `cyclotomic n R` is the minimal polynomial of a primitive
 root of unity.

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

@@ -4,11 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 
 ! This file was ported from Lean 3 source module ring_theory.polynomial.cyclotomic.roots
-! leanprover-community/mathlib commit 5bfbcca0a7ffdd21cf1682e59106d6c942434a32
+! leanprover-community/mathlib commit 7fdeecc0d03cd40f7a165e6cf00a4d2286db599f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Polynomial.Cyclotomic.Basic
+import Mathbin.RingTheory.RootsOfUnity.Minpoly
 
 /-!
 # Roots of cyclotomic polynomials.
@@ -49,7 +50,7 @@ theorem isRoot_of_unity_of_root_cyclotomic {ζ : R} {i : ℕ} (hi : i ∈ n.divi
   have := congr_arg (eval ζ) (prod_cyclotomic_eq_X_pow_sub_one hn R).symm
   rw [eval_sub, eval_pow, eval_X, eval_one] at this 
   convert eq_add_of_sub_eq' this
-  convert(add_zero _).symm
+  convert (add_zero _).symm
   apply eval_eq_zero_of_dvd_of_eval_eq_zero _ h
   exact Finset.dvd_prod_of_mem _ hi
 #align polynomial.is_root_of_unity_of_root_cyclotomic Polynomial.isRoot_of_unity_of_root_cyclotomic

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

@@ -47,7 +47,7 @@ theorem isRoot_of_unity_of_root_cyclotomic {ζ : R} {i : ℕ} (hi : i ∈ n.divi
   rcases n.eq_zero_or_pos with (rfl | hn)
   · exact pow_zero _
   have := congr_arg (eval ζ) (prod_cyclotomic_eq_X_pow_sub_one hn R).symm
-  rw [eval_sub, eval_pow, eval_X, eval_one] at this
+  rw [eval_sub, eval_pow, eval_X, eval_one] at this 
   convert eq_add_of_sub_eq' this
   convert(add_zero _).symm
   apply eval_eq_zero_of_dvd_of_eval_eq_zero _ h
@@ -71,7 +71,7 @@ theorem IsPrimitiveRoot.isRoot_cyclotomic (hpos : 0 < n) {μ : R} (h : IsPrimiti
   by
   rw [← mem_roots (cyclotomic_ne_zero n R), cyclotomic_eq_prod_X_sub_primitive_roots h,
     roots_prod_X_sub_C, ← Finset.mem_def]
-  rwa [← mem_primitiveRoots hpos] at h
+  rwa [← mem_primitiveRoots hpos] at h 
 #align is_primitive_root.is_root_cyclotomic IsPrimitiveRoot.isRoot_cyclotomic
 
 private theorem is_root_cyclotomic_iff' {n : ℕ} {K : Type _} [Field K] {μ : K} [NeZero (n : K)] :
@@ -90,21 +90,21 @@ private theorem is_root_cyclotomic_iff' {n : ℕ} {K : Type _} [Field K] {μ : K
     rw [isOfFinOrder_iff_pow_eq_one]
     exact ⟨n, hnpos, hμn⟩
   have := pow_orderOf_eq_one μ
-  rw [isRoot_of_unity_iff ho] at this
+  rw [isRoot_of_unity_iff ho] at this 
   obtain ⟨i, hio, hiμ⟩ := this
   replace hio := Nat.dvd_of_mem_divisors hio
-  rw [IsPrimitiveRoot.not_iff] at hnμ
-  rw [← orderOf_dvd_iff_pow_eq_one] at hμn
+  rw [IsPrimitiveRoot.not_iff] at hnμ 
+  rw [← orderOf_dvd_iff_pow_eq_one] at hμn 
   have key : i < n := (Nat.le_of_dvd ho hio).trans_lt ((Nat.le_of_dvd hnpos hμn).lt_of_ne hnμ)
   have key' : i ∣ n := hio.trans hμn
-  rw [← Polynomial.dvd_iff_isRoot] at hμ hiμ
+  rw [← Polynomial.dvd_iff_isRoot] at hμ hiμ 
   have hni : {i, n} ⊆ n.divisors := by simpa [Finset.insert_subset, key'] using hnpos.ne'
   obtain ⟨k, hk⟩ := hiμ
   obtain ⟨j, hj⟩ := hμ
   have := prod_cyclotomic_eq_X_pow_sub_one hnpos K
-  rw [← Finset.prod_sdiff hni, Finset.prod_pair key.ne, hk, hj] at this
+  rw [← Finset.prod_sdiff hni, Finset.prod_pair key.ne, hk, hj] at this 
   have hn := (X_pow_sub_one_separable_iff.mpr <| NeZero.natCast_ne n K).Squarefree
-  rw [← this, Squarefree] at hn
+  rw [← this, Squarefree] at hn 
   contrapose! hn
   refine' ⟨X - C μ, ⟨(∏ x in n.divisors \ {i, n}, cyclotomic x K) * k * j, by ring⟩, _⟩
   simp [Polynomial.isUnit_iff_degree_eq_zero]
@@ -123,7 +123,7 @@ theorem roots_cyclotomic_nodup [NeZero (n : R)] : (cyclotomic n R).roots.Nodup :
   by
   obtain h | ⟨ζ, hζ⟩ := (cyclotomic n R).roots.empty_or_exists_mem
   · exact h.symm ▸ Multiset.nodup_zero
-  rw [mem_roots <| cyclotomic_ne_zero n R, is_root_cyclotomic_iff] at hζ
+  rw [mem_roots <| cyclotomic_ne_zero n R, is_root_cyclotomic_iff] at hζ 
   refine'
     Multiset.nodup_of_le
       (roots.le_of_dvd (X_pow_sub_C_ne_zero (NeZero.pos_of_neZero_natCast R) 1) <|
@@ -156,25 +156,25 @@ end IsDomain
 theorem cyclotomic_injective [CharZero R] : Function.Injective fun n => cyclotomic n R :=
   by
   intro n m hnm
-  simp only at hnm
+  simp only at hnm 
   rcases eq_or_ne n 0 with (rfl | hzero)
-  · rw [cyclotomic_zero] at hnm
+  · rw [cyclotomic_zero] at hnm 
     replace hnm := congr_arg nat_degree hnm
-    rw [nat_degree_one, nat_degree_cyclotomic] at hnm
+    rw [nat_degree_one, nat_degree_cyclotomic] at hnm 
     by_contra
     exact (Nat.totient_pos (zero_lt_iff.2 (Ne.symm h))).Ne hnm
   · haveI := NeZero.mk hzero
-    rw [← map_cyclotomic_int _ R, ← map_cyclotomic_int _ R] at hnm
+    rw [← map_cyclotomic_int _ R, ← map_cyclotomic_int _ R] at hnm 
     replace hnm := map_injective (Int.castRingHom R) Int.cast_injective hnm
     replace hnm := congr_arg (map (Int.castRingHom ℂ)) hnm
-    rw [map_cyclotomic_int, map_cyclotomic_int] at hnm
+    rw [map_cyclotomic_int, map_cyclotomic_int] at hnm 
     have hprim := Complex.isPrimitiveRoot_exp _ hzero
     have hroot := is_root_cyclotomic_iff.2 hprim
-    rw [hnm] at hroot
+    rw [hnm] at hroot 
     haveI hmzero : NeZero m := ⟨fun h => by simpa [h] using hroot⟩
-    rw [is_root_cyclotomic_iff] at hroot
+    rw [is_root_cyclotomic_iff] at hroot 
     replace hprim := hprim.eq_order_of
-    rwa [← IsPrimitiveRoot.eq_orderOf hroot] at hprim
+    rwa [← IsPrimitiveRoot.eq_orderOf hroot] at hprim 
 #align polynomial.cyclotomic_injective Polynomial.cyclotomic_injective
 
 /-- The minimal polynomial of a primitive `n`-th root of unity `μ` divides `cyclotomic n ℤ`. -/

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

@@ -35,7 +35,7 @@ primitive root of unity `μ : K`, where `K` is a field of characteristic `0`.
 -/
 
 
-open BigOperators
+open scoped BigOperators
 
 namespace Polynomial
 

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

@@ -132,9 +132,7 @@ theorem roots_cyclotomic_nodup [NeZero (n : R)] : (cyclotomic n R).roots.Nodup :
 #align polynomial.roots_cyclotomic_nodup Polynomial.roots_cyclotomic_nodup
 
 theorem cyclotomic.roots_to_finset_eq_primitiveRoots [NeZero (n : R)] :
-    (⟨(cyclotomic n R).roots, roots_cyclotomic_nodup⟩ : Finset _) = primitiveRoots n R :=
-  by
-  ext
+    (⟨(cyclotomic n R).roots, roots_cyclotomic_nodup⟩ : Finset _) = primitiveRoots n R := by ext;
   simp [cyclotomic_ne_zero n R, is_root_cyclotomic_iff, mem_primitiveRoots,
     NeZero.pos_of_neZero_natCast R]
 #align polynomial.cyclotomic.roots_to_finset_eq_primitive_roots Polynomial.cyclotomic.roots_to_finset_eq_primitiveRoots

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

@@ -109,7 +109,6 @@ private theorem is_root_cyclotomic_iff' {n : ℕ} {K : Type _} [Field K] {μ : K
   refine' ⟨X - C μ, ⟨(∏ x in n.divisors \ {i, n}, cyclotomic x K) * k * j, by ring⟩, _⟩
   simp [Polynomial.isUnit_iff_degree_eq_zero]
   all_goals infer_instance
-#align polynomial.is_root_cyclotomic_iff' polynomial.is_root_cyclotomic_iff'
 
 theorem isRoot_cyclotomic_iff [NeZero (n : R)] {μ : R} :
     IsRoot (cyclotomic n R) μ ↔ IsPrimitiveRoot μ n :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -169,7 +169,7 @@ theorem cyclotomic_injective [CharZero R] : Function.Injective fun n => cyclotom
 theorem _root_.IsPrimitiveRoot.minpoly_dvd_cyclotomic {n : ℕ} {K : Type*} [Field K] {μ : K}
     (h : IsPrimitiveRoot μ n) (hpos : 0 < n) [CharZero K] : minpoly ℤ μ ∣ cyclotomic n ℤ := by
   apply minpoly.isIntegrallyClosed_dvd (h.isIntegral hpos)
-  simpa [aeval_def, eval₂_eq_eval_map, IsRoot.definition] using h.isRoot_cyclotomic hpos
+  simpa [aeval_def, eval₂_eq_eval_map, IsRoot.def] using h.isRoot_cyclotomic hpos
 #align is_primitive_root.minpoly_dvd_cyclotomic IsPrimitiveRoot.minpoly_dvd_cyclotomic
 
 section minpoly
@@ -181,7 +181,7 @@ theorem _root_.IsPrimitiveRoot.minpoly_eq_cyclotomic_of_irreducible {K : Type*}
     (h : Irreducible <| cyclotomic n K) [NeZero (n : K)] : cyclotomic n K = minpoly K μ := by
   haveI := NeZero.of_noZeroSMulDivisors K R n
   refine' minpoly.eq_of_irreducible_of_monic h _ (cyclotomic.monic n K)
-  rwa [aeval_def, eval₂_eq_eval_map, map_cyclotomic, ← IsRoot.definition, isRoot_cyclotomic_iff]
+  rwa [aeval_def, eval₂_eq_eval_map, map_cyclotomic, ← IsRoot.def, isRoot_cyclotomic_iff]
 #align is_primitive_root.minpoly_eq_cyclotomic_of_irreducible IsPrimitiveRoot.minpoly_eq_cyclotomic_of_irreducible
 
 /-- `cyclotomic n ℤ` is the minimal polynomial of a primitive `n`-th root of unity `μ`. -/

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -61,7 +61,7 @@ theorem _root_.isRoot_of_unity_iff (h : 0 < n) (R : Type*) [CommRing R] [IsDomai
       prod_cyclotomic_eq_X_pow_sub_one h, isRoot_prod]
 #align is_root_of_unity_iff isRoot_of_unity_iff
 
-/-- Any `n`-th primitive root of unity is a root of `cyclotomic n R`.-/
+/-- Any `n`-th primitive root of unity is a root of `cyclotomic n R`. -/
 theorem _root_.IsPrimitiveRoot.isRoot_cyclotomic (hpos : 0 < n) {μ : R} (h : IsPrimitiveRoot μ n) :
     IsRoot (cyclotomic n R) μ := by
   rw [← mem_roots (cyclotomic_ne_zero n R), cyclotomic_eq_prod_X_sub_primitiveRoots h,

These will be caught by the linter in a future lean version.

@@ -95,9 +95,8 @@ private theorem isRoot_cyclotomic_iff' {n : ℕ} {K : Type*} [Field K] {μ : K}
   rw [← Finset.prod_sdiff hni, Finset.prod_pair key.ne, hk, hj] at this
   have hn := (X_pow_sub_one_separable_iff.mpr <| NeZero.natCast_ne n K).squarefree
   rw [← this, Squarefree] at hn
-  contrapose! hn
-  refine' ⟨X - C μ, ⟨(∏ x in n.divisors \ {i, n}, cyclotomic x K) * k * j, by ring⟩, _⟩
-  simp [Polynomial.isUnit_iff_degree_eq_zero]
+  specialize hn (X - C μ) ⟨(∏ x in n.divisors \ {i, n}, cyclotomic x K) * k * j, by ring⟩
+  simp [Polynomial.isUnit_iff_degree_eq_zero] at hn
 
 theorem isRoot_cyclotomic_iff [NeZero (n : R)] {μ : R} :
     IsRoot (cyclotomic n R) μ ↔ IsPrimitiveRoot μ n := by

This will become an error in 2024-03-16 nightly, possibly not permanently.

Co-authored-by: Scott Morrison <scott@tqft.net>

@@ -170,7 +170,7 @@ theorem cyclotomic_injective [CharZero R] : Function.Injective fun n => cyclotom
 theorem _root_.IsPrimitiveRoot.minpoly_dvd_cyclotomic {n : ℕ} {K : Type*} [Field K] {μ : K}
     (h : IsPrimitiveRoot μ n) (hpos : 0 < n) [CharZero K] : minpoly ℤ μ ∣ cyclotomic n ℤ := by
   apply minpoly.isIntegrallyClosed_dvd (h.isIntegral hpos)
-  simpa [aeval_def, eval₂_eq_eval_map, IsRoot.def] using h.isRoot_cyclotomic hpos
+  simpa [aeval_def, eval₂_eq_eval_map, IsRoot.definition] using h.isRoot_cyclotomic hpos
 #align is_primitive_root.minpoly_dvd_cyclotomic IsPrimitiveRoot.minpoly_dvd_cyclotomic
 
 section minpoly
@@ -182,7 +182,7 @@ theorem _root_.IsPrimitiveRoot.minpoly_eq_cyclotomic_of_irreducible {K : Type*}
     (h : Irreducible <| cyclotomic n K) [NeZero (n : K)] : cyclotomic n K = minpoly K μ := by
   haveI := NeZero.of_noZeroSMulDivisors K R n
   refine' minpoly.eq_of_irreducible_of_monic h _ (cyclotomic.monic n K)
-  rwa [aeval_def, eval₂_eq_eval_map, map_cyclotomic, ← IsRoot.def, isRoot_cyclotomic_iff]
+  rwa [aeval_def, eval₂_eq_eval_map, map_cyclotomic, ← IsRoot.definition, isRoot_cyclotomic_iff]
 #align is_primitive_root.minpoly_eq_cyclotomic_of_irreducible IsPrimitiveRoot.minpoly_eq_cyclotomic_of_irreducible
 
 /-- `cyclotomic n ℤ` is the minimal polynomial of a primitive `n`-th root of unity `μ`. -/

See Zulip thread for the discussion.

@@ -78,7 +78,7 @@ private theorem isRoot_cyclotomic_iff' {n : ℕ} {K : Type*} [Field K] {μ : K}
     rw [isRoot_of_unity_iff hnpos _]
     exact ⟨n, n.mem_divisors_self hnpos.ne', hμ⟩
   by_contra hnμ
-  have ho : 0 < orderOf μ := (isOfFinOrder_iff_pow_eq_one.2 $ ⟨n, hnpos, hμn⟩).orderOf_pos
+  have ho : 0 < orderOf μ := (isOfFinOrder_iff_pow_eq_one.2 <| ⟨n, hnpos, hμn⟩).orderOf_pos
   have := pow_orderOf_eq_one μ
   rw [isRoot_of_unity_iff ho] at this
   obtain ⟨i, hio, hiμ⟩ := this

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

@@ -113,7 +113,7 @@ theorem roots_cyclotomic_nodup [NeZero (n : R)] : (cyclotomic n R).roots.Nodup :
   rw [mem_roots <| cyclotomic_ne_zero n R, isRoot_cyclotomic_iff] at hζ
   refine' Multiset.nodup_of_le
     (roots.le_of_dvd (X_pow_sub_C_ne_zero (NeZero.pos_of_neZero_natCast R) 1) <|
-      cyclotomic.dvd_X_pow_sub_one n R) hζ.nthRoots_nodup
+      cyclotomic.dvd_X_pow_sub_one n R) hζ.nthRoots_one_nodup
 #align polynomial.roots_cyclotomic_nodup Polynomial.roots_cyclotomic_nodup
 
 theorem cyclotomic.roots_to_finset_eq_primitiveRoots [NeZero (n : R)] :

Many lemmas in GroupTheory.OrderOfElement were stated for elements of finite groups even though they work more generally for torsion elements of possibly infinite groups. This PR generalises those lemmas (and leaves convenience lemmas stated for finite groups), and fixes a bunch of names to use dot notation.

Renames

• Function.eq_of_lt_minimalPeriod_of_iterate_eq → Function.iterate_injOn_Iio_minimalPeriod
• Function.eq_iff_lt_minimalPeriod_of_iterate_eq → Function.iterate_eq_iterate_iff_of_lt_minimalPeriod
• isOfFinOrder_iff_coe → Submonoid.isOfFinOrder_coe
• orderOf_pos' → IsOfFinOrder.orderOf_pos
• pow_eq_mod_orderOf → pow_mod_orderOf (and turned around)
• pow_injective_of_lt_orderOf → pow_injOn_Iio_orderOf
• mem_powers_iff_mem_range_order_of' → IsOfFinOrder.mem_powers_iff_mem_range_orderOf
• orderOf_pow'' → IsOfFinOrder.orderOf_pow
• orderOf_pow_coprime → Nat.Coprime.orderOf_pow
• zpow_eq_mod_orderOf → zpow_mod_orderOf (and turned around)
• exists_pow_eq_one → isOfFinOrder_of_finite
• pow_apply_eq_pow_mod_orderOf_cycleOf_apply → pow_mod_orderOf_cycleOf_apply

New lemmas

• IsOfFinOrder.powers_eq_image_range_orderOf
• IsOfFinOrder.natCard_powers_le_orderOf
• IsOfFinOrder.finite_powers
• finite_powers
• infinite_powers
• Nat.card_submonoidPowers
• IsOfFinOrder.mem_powers_iff_mem_zpowers
• IsOfFinOrder.powers_eq_zpowers
• IsOfFinOrder.mem_zpowers_iff_mem_range_orderOf
• IsOfFinOrder.exists_pow_eq_one

Other changes

• Move decidableMemPowers/fintypePowers to GroupTheory.Submonoid.Membership and decidableMemZpowers/fintypeZpowers to GroupTheory.Subgroup.ZPowers.
• finEquivPowers, finEquivZpowers, powersEquivPowers and zpowersEquivZpowers now assume IsOfFinTorsion x instead of Finite G.
• isOfFinOrder_iff_pow_eq_one now takes one less explicit argument.
• Delete Equiv.Perm.IsCycle.exists_pow_eq_one since it was saying that a permutation over a finite type is torsion, but this is trivial since the group of permutation is itself finite, so we can use isOfFinOrder_of_finite instead.

@@ -78,10 +78,7 @@ private theorem isRoot_cyclotomic_iff' {n : ℕ} {K : Type*} [Field K] {μ : K}
     rw [isRoot_of_unity_iff hnpos _]
     exact ⟨n, n.mem_divisors_self hnpos.ne', hμ⟩
   by_contra hnμ
-  have ho : 0 < orderOf μ := by
-    apply orderOf_pos'
-    rw [isOfFinOrder_iff_pow_eq_one]
-    exact ⟨n, hnpos, hμn⟩
+  have ho : 0 < orderOf μ := (isOfFinOrder_iff_pow_eq_one.2 $ ⟨n, hnpos, hμn⟩).orderOf_pos
   have := pow_orderOf_eq_one μ
   rw [isRoot_of_unity_iff ho] at this
   obtain ⟨i, hio, hiμ⟩ := this

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -37,7 +37,7 @@ open scoped BigOperators
 
 namespace Polynomial
 
-variable {R : Type _} [CommRing R] {n : ℕ}
+variable {R : Type*} [CommRing R] {n : ℕ}
 
 theorem isRoot_of_unity_of_root_cyclotomic {ζ : R} {i : ℕ} (hi : i ∈ n.divisors)
     (h : (cyclotomic i R).IsRoot ζ) : ζ ^ n = 1 := by
@@ -55,7 +55,7 @@ section IsDomain
 
 variable [IsDomain R]
 
-theorem _root_.isRoot_of_unity_iff (h : 0 < n) (R : Type _) [CommRing R] [IsDomain R] {ζ : R} :
+theorem _root_.isRoot_of_unity_iff (h : 0 < n) (R : Type*) [CommRing R] [IsDomain R] {ζ : R} :
     ζ ^ n = 1 ↔ ∃ i ∈ n.divisors, (cyclotomic i R).IsRoot ζ := by
   rw [← mem_nthRoots h, nthRoots, mem_roots <| X_pow_sub_C_ne_zero h _, C_1, ←
       prod_cyclotomic_eq_X_pow_sub_one h, isRoot_prod]
@@ -69,7 +69,7 @@ theorem _root_.IsPrimitiveRoot.isRoot_cyclotomic (hpos : 0 < n) {μ : R} (h : Is
   rwa [← mem_primitiveRoots hpos] at h
 #align is_primitive_root.is_root_cyclotomic IsPrimitiveRoot.isRoot_cyclotomic
 
-private theorem isRoot_cyclotomic_iff' {n : ℕ} {K : Type _} [Field K] {μ : K} [NeZero (n : K)] :
+private theorem isRoot_cyclotomic_iff' {n : ℕ} {K : Type*} [Field K] {μ : K} [NeZero (n : K)] :
     IsRoot (cyclotomic n K) μ ↔ IsPrimitiveRoot μ n := by
   -- in this proof, `o` stands for `orderOf μ`
   have hnpos : 0 < n := (NeZero.of_neZero_natCast K).out.bot_lt
@@ -137,7 +137,7 @@ theorem cyclotomic.roots_eq_primitiveRoots_val [NeZero (n : R)] :
 
 /-- If `R` is of characteristic zero, then `ζ` is a root of `cyclotomic n R` if and only if it is a
 primitive `n`-th root of unity. -/
-theorem isRoot_cyclotomic_iff_charZero {n : ℕ} {R : Type _} [CommRing R] [IsDomain R] [CharZero R]
+theorem isRoot_cyclotomic_iff_charZero {n : ℕ} {R : Type*} [CommRing R] [IsDomain R] [CharZero R]
     {μ : R} (hn : 0 < n) : (Polynomial.cyclotomic n R).IsRoot μ ↔ IsPrimitiveRoot μ n :=
   letI := NeZero.of_gt hn
   isRoot_cyclotomic_iff
@@ -170,7 +170,7 @@ theorem cyclotomic_injective [CharZero R] : Function.Injective fun n => cyclotom
 #align polynomial.cyclotomic_injective Polynomial.cyclotomic_injective
 
 /-- The minimal polynomial of a primitive `n`-th root of unity `μ` divides `cyclotomic n ℤ`. -/
-theorem _root_.IsPrimitiveRoot.minpoly_dvd_cyclotomic {n : ℕ} {K : Type _} [Field K] {μ : K}
+theorem _root_.IsPrimitiveRoot.minpoly_dvd_cyclotomic {n : ℕ} {K : Type*} [Field K] {μ : K}
     (h : IsPrimitiveRoot μ n) (hpos : 0 < n) [CharZero K] : minpoly ℤ μ ∣ cyclotomic n ℤ := by
   apply minpoly.isIntegrallyClosed_dvd (h.isIntegral hpos)
   simpa [aeval_def, eval₂_eq_eval_map, IsRoot.def] using h.isRoot_cyclotomic hpos
@@ -180,8 +180,8 @@ section minpoly
 
 open IsPrimitiveRoot Complex
 
-theorem _root_.IsPrimitiveRoot.minpoly_eq_cyclotomic_of_irreducible {K : Type _} [Field K]
-    {R : Type _} [CommRing R] [IsDomain R] {μ : R} {n : ℕ} [Algebra K R] (hμ : IsPrimitiveRoot μ n)
+theorem _root_.IsPrimitiveRoot.minpoly_eq_cyclotomic_of_irreducible {K : Type*} [Field K]
+    {R : Type*} [CommRing R] [IsDomain R] {μ : R} {n : ℕ} [Algebra K R] (hμ : IsPrimitiveRoot μ n)
     (h : Irreducible <| cyclotomic n K) [NeZero (n : K)] : cyclotomic n K = minpoly K μ := by
   haveI := NeZero.of_noZeroSMulDivisors K R n
   refine' minpoly.eq_of_irreducible_of_monic h _ (cyclotomic.monic n K)
@@ -189,7 +189,7 @@ theorem _root_.IsPrimitiveRoot.minpoly_eq_cyclotomic_of_irreducible {K : Type _}
 #align is_primitive_root.minpoly_eq_cyclotomic_of_irreducible IsPrimitiveRoot.minpoly_eq_cyclotomic_of_irreducible
 
 /-- `cyclotomic n ℤ` is the minimal polynomial of a primitive `n`-th root of unity `μ`. -/
-theorem cyclotomic_eq_minpoly {n : ℕ} {K : Type _} [Field K] {μ : K} (h : IsPrimitiveRoot μ n)
+theorem cyclotomic_eq_minpoly {n : ℕ} {K : Type*} [Field K] {μ : K} (h : IsPrimitiveRoot μ n)
     (hpos : 0 < n) [CharZero K] : cyclotomic n ℤ = minpoly ℤ μ := by
   refine' eq_of_monic_of_dvd_of_natDegree_le (minpoly.monic (IsPrimitiveRoot.isIntegral h hpos))
     (cyclotomic.monic n ℤ) (h.minpoly_dvd_cyclotomic hpos) _
@@ -197,7 +197,7 @@ theorem cyclotomic_eq_minpoly {n : ℕ} {K : Type _} [Field K] {μ : K} (h : IsP
 #align polynomial.cyclotomic_eq_minpoly Polynomial.cyclotomic_eq_minpoly
 
 /-- `cyclotomic n ℚ` is the minimal polynomial of a primitive `n`-th root of unity `μ`. -/
-theorem cyclotomic_eq_minpoly_rat {n : ℕ} {K : Type _} [Field K] {μ : K} (h : IsPrimitiveRoot μ n)
+theorem cyclotomic_eq_minpoly_rat {n : ℕ} {K : Type*} [Field K] {μ : K} (h : IsPrimitiveRoot μ n)
     (hpos : 0 < n) [CharZero K] : cyclotomic n ℚ = minpoly ℚ μ := by
   rw [← map_cyclotomic_int, cyclotomic_eq_minpoly h hpos]
   exact (minpoly.isIntegrallyClosed_eq_field_fractions' _ (IsPrimitiveRoot.isIntegral h hpos)).symm

• 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) 2020 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 ring_theory.polynomial.cyclotomic.roots
-! leanprover-community/mathlib commit 7fdeecc0d03cd40f7a165e6cf00a4d2286db599f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.Polynomial.Cyclotomic.Basic
 import Mathlib.RingTheory.RootsOfUnity.Minpoly
 
+#align_import ring_theory.polynomial.cyclotomic.roots from "leanprover-community/mathlib"@"7fdeecc0d03cd40f7a165e6cf00a4d2286db599f"
+
 /-!
 # Roots of cyclotomic polynomials.
 

Currently, (for both Set and Finset) insert_subset is an iff lemma stating that insert a s ⊆ t if and only if a ∈ t and s ⊆ t. For both types, this PR renames this lemma to insert_subset_iff, and adds an insert_subset lemma that gives the implication just in the reverse direction : namely theorem insert_subset (ha : a ∈ t) (hs : s ⊆ t) : insert a s ⊆ t .

This both aligns the naming with union_subset and union_subset_iff, and removes the need for the awkward insert_subset.mpr ⟨_,_⟩ idiom. It touches a lot of files (too many to list), but in a trivial way.

@@ -94,7 +94,7 @@ private theorem isRoot_cyclotomic_iff' {n : ℕ} {K : Type _} [Field K] {μ : K}
   have key : i < n := (Nat.le_of_dvd ho hio).trans_lt ((Nat.le_of_dvd hnpos hμn).lt_of_ne hnμ)
   have key' : i ∣ n := hio.trans hμn
   rw [← Polynomial.dvd_iff_isRoot] at hμ hiμ
-  have hni : {i, n} ⊆ n.divisors := by simpa [Finset.insert_subset, key'] using hnpos.ne'
+  have hni : {i, n} ⊆ n.divisors := by simpa [Finset.insert_subset_iff, key'] using hnpos.ne'
   obtain ⟨k, hk⟩ := hiμ
   obtain ⟨j, hj⟩ := hμ
   have := prod_cyclotomic_eq_X_pow_sub_one hnpos K

@@ -72,7 +72,7 @@ theorem _root_.IsPrimitiveRoot.isRoot_cyclotomic (hpos : 0 < n) {μ : R} (h : Is
   rwa [← mem_primitiveRoots hpos] at h
 #align is_primitive_root.is_root_cyclotomic IsPrimitiveRoot.isRoot_cyclotomic
 
-private theorem is_root_cyclotomic_iff' {n : ℕ} {K : Type _} [Field K] {μ : K} [NeZero (n : K)] :
+private theorem isRoot_cyclotomic_iff' {n : ℕ} {K : Type _} [Field K] {μ : K} [NeZero (n : K)] :
     IsRoot (cyclotomic n K) μ ↔ IsPrimitiveRoot μ n := by
   -- in this proof, `o` stands for `orderOf μ`
   have hnpos : 0 < n := (NeZero.of_neZero_natCast K).out.bot_lt
@@ -110,7 +110,7 @@ theorem isRoot_cyclotomic_iff [NeZero (n : R)] {μ : R} :
   have hf : Function.Injective _ := IsFractionRing.injective R (FractionRing R)
   haveI : NeZero (n : FractionRing R) := NeZero.nat_of_injective hf
   rw [← isRoot_map_iff hf, ← IsPrimitiveRoot.map_iff_of_injective hf, map_cyclotomic, ←
-    is_root_cyclotomic_iff']
+    isRoot_cyclotomic_iff']
 #align polynomial.is_root_cyclotomic_iff Polynomial.isRoot_cyclotomic_iff
 
 theorem roots_cyclotomic_nodup [NeZero (n : R)] : (cyclotomic n R).roots.Nodup := by