ring_theory.polynomial.cyclotomic.expand ⟷ Mathlib.RingTheory.Polynomial.Cyclotomic.Expand

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

@@ -123,7 +123,7 @@ theorem cyclotomic_irreducible_pow_of_irreducible_pow {p : ℕ} (hp : Nat.Prime
   induction' k with k hk
   · simpa using h
   have : m + k ≠ 0 := (add_pos_of_pos_of_nonneg hm k.zero_le).ne'
-  rw [Nat.add_succ, pow_succ', ← cyclotomic_expand_eq_cyclotomic hp <| dvd_pow_self p this] at h
+  rw [Nat.add_succ, pow_succ, ← cyclotomic_expand_eq_cyclotomic hp <| dvd_pow_self p this] at h
   exact hk (by linarith) (of_irreducible_expand hp.ne_zero h)
 #align polynomial.cyclotomic_irreducible_pow_of_irreducible_pow Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow
 -/
@@ -150,7 +150,7 @@ theorem cyclotomic_mul_prime_eq_pow_of_not_dvd (R : Type _) {p n : ℕ} [hp : Fa
     rw [← map_cyclotomic _ (algebraMap (ZMod p) R), ← map_cyclotomic _ (algebraMap (ZMod p) R),
       this, Polynomial.map_pow]
   apply mul_right_injective₀ (cyclotomic_ne_zero n <| ZMod p)
-  rw [← pow_succ, tsub_add_cancel_of_le hp.out.one_lt.le, mul_comm, ← ZMod.expand_card]
+  rw [← pow_succ', tsub_add_cancel_of_le hp.out.one_lt.le, mul_comm, ← ZMod.expand_card]
   nth_rw 3 [← map_cyclotomic_int]
   rw [← map_expand, cyclotomic_expand_eq_cyclotomic_mul hp.out hn, Polynomial.map_mul,
     map_cyclotomic, map_cyclotomic]
@@ -181,12 +181,12 @@ theorem cyclotomic_mul_prime_pow_eq (R : Type _) {p m : ℕ} [Fact (Nat.Prime p)
     rw [pow_one, Nat.sub_self, pow_zero, mul_comm, cyclotomic_mul_prime_eq_pow_of_not_dvd R hm]
   | a + 2, _ =>
     by
-    have hdiv : p ∣ p ^ a.succ * m := ⟨p ^ a * m, by rw [← mul_assoc, pow_succ]⟩
-    rw [pow_succ, mul_assoc, mul_comm, cyclotomic_mul_prime_dvd_eq_pow R hdiv,
+    have hdiv : p ∣ p ^ a.succ * m := ⟨p ^ a * m, by rw [← mul_assoc, pow_succ']⟩
+    rw [pow_succ', mul_assoc, mul_comm, cyclotomic_mul_prime_dvd_eq_pow R hdiv,
       cyclotomic_mul_prime_pow_eq a.succ_pos, ← pow_mul]
     congr 1
     simp only [tsub_zero, Nat.succ_sub_succ_eq_sub]
-    rw [Nat.mul_sub_right_distrib, mul_comm, pow_succ']
+    rw [Nat.mul_sub_right_distrib, mul_comm, pow_succ]
 #align polynomial.cyclotomic_mul_prime_pow_eq Polynomial.cyclotomic_mul_prime_pow_eq
 -/
 

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

@@ -123,7 +123,7 @@ theorem cyclotomic_irreducible_pow_of_irreducible_pow {p : ℕ} (hp : Nat.Prime
   induction' k with k hk
   · simpa using h
   have : m + k ≠ 0 := (add_pos_of_pos_of_nonneg hm k.zero_le).ne'
-  rw [Nat.add_succ, pow_succ', ← cyclotomic_expand_eq_cyclotomic hp <| dvd_pow_self p this] at h 
+  rw [Nat.add_succ, pow_succ', ← cyclotomic_expand_eq_cyclotomic hp <| dvd_pow_self p this] at h
   exact hk (by linarith) (of_irreducible_expand hp.ne_zero h)
 #align polynomial.cyclotomic_irreducible_pow_of_irreducible_pow Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow
 -/
@@ -201,10 +201,10 @@ theorem isRoot_cyclotomic_prime_pow_mul_iff_of_charP {m k p : ℕ} {R : Type _}
   rcases k.eq_zero_or_pos with (rfl | hk)
   · rw [pow_zero, one_mul, is_root_cyclotomic_iff]
   refine' ⟨fun h => _, fun h => _⟩
-  · rw [is_root.def, cyclotomic_mul_prime_pow_eq R (NeZero.not_char_dvd R p m) hk, eval_pow] at h 
+  · rw [is_root.def, cyclotomic_mul_prime_pow_eq R (NeZero.not_char_dvd R p m) hk, eval_pow] at h
     replace h := pow_eq_zero h
-    rwa [← is_root.def, is_root_cyclotomic_iff] at h 
-  · rw [← is_root_cyclotomic_iff, is_root.def] at h 
+    rwa [← is_root.def, is_root_cyclotomic_iff] at h
+  · rw [← is_root_cyclotomic_iff, is_root.def] at h
     rw [cyclotomic_mul_prime_pow_eq R (NeZero.not_char_dvd R p m) hk, is_root.def, eval_pow, h,
       zero_pow]
     simp only [tsub_pos_iff_lt]

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

@@ -208,7 +208,7 @@ theorem isRoot_cyclotomic_prime_pow_mul_iff_of_charP {m k p : ℕ} {R : Type _}
     rw [cyclotomic_mul_prime_pow_eq R (NeZero.not_char_dvd R p m) hk, is_root.def, eval_pow, h,
       zero_pow]
     simp only [tsub_pos_iff_lt]
-    apply pow_strictMono_right hp.out.one_lt (Nat.pred_lt hk.ne')
+    apply pow_right_strictMono hp.out.one_lt (Nat.pred_lt hk.ne')
 #align polynomial.is_root_cyclotomic_prime_pow_mul_iff_of_char_p Polynomial.isRoot_cyclotomic_prime_pow_mul_iff_of_charP
 -/
 

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

@@ -3,7 +3,7 @@ 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.Roots
+import RingTheory.Polynomial.Cyclotomic.Roots
 
 #align_import ring_theory.polynomial.cyclotomic.expand from "leanprover-community/mathlib"@"0723536a0522d24fc2f159a096fb3304bef77472"
 

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

@@ -2,14 +2,11 @@
 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.expand
-! leanprover-community/mathlib commit 0723536a0522d24fc2f159a096fb3304bef77472
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Polynomial.Cyclotomic.Roots
 
+#align_import ring_theory.polynomial.cyclotomic.expand from "leanprover-community/mathlib"@"0723536a0522d24fc2f159a096fb3304bef77472"
+
 /-!
 # Cyclotomic polynomials and `expand`.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/0723536a0522d24fc2f159a096fb3304bef77472

@@ -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.expand
-! leanprover-community/mathlib commit 2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
+! leanprover-community/mathlib commit 0723536a0522d24fc2f159a096fb3304bef77472
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -148,6 +148,7 @@ section CharP
 theorem cyclotomic_mul_prime_eq_pow_of_not_dvd (R : Type _) {p n : ℕ} [hp : Fact (Nat.Prime p)]
     [Ring R] [CharP R p] (hn : ¬p ∣ n) : cyclotomic (n * p) R = cyclotomic n R ^ (p - 1) :=
   by
+  letI : Algebra (ZMod p) R := ZMod.algebra _ _
   suffices cyclotomic (n * p) (ZMod p) = cyclotomic n (ZMod p) ^ (p - 1) by
     rw [← map_cyclotomic _ (algebraMap (ZMod p) R), ← map_cyclotomic _ (algebraMap (ZMod p) R),
       this, Polynomial.map_pow]
@@ -165,6 +166,7 @@ theorem cyclotomic_mul_prime_eq_pow_of_not_dvd (R : Type _) {p n : ℕ} [hp : Fa
 theorem cyclotomic_mul_prime_dvd_eq_pow (R : Type _) {p n : ℕ} [hp : Fact (Nat.Prime p)] [Ring R]
     [CharP R p] (hn : p ∣ n) : cyclotomic (n * p) R = cyclotomic n R ^ p :=
   by
+  letI : Algebra (ZMod p) R := ZMod.algebra _ _
   suffices cyclotomic (n * p) (ZMod p) = cyclotomic n (ZMod p) ^ p by
     rw [← map_cyclotomic _ (algebraMap (ZMod p) R), ← map_cyclotomic _ (algebraMap (ZMod p) R),
       this, Polynomial.map_pow]
@@ -198,6 +200,7 @@ theorem isRoot_cyclotomic_prime_pow_mul_iff_of_charP {m k p : ℕ} {R : Type _}
     [IsDomain R] [hp : Fact (Nat.Prime p)] [hchar : CharP R p] {μ : R} [NeZero (m : R)] :
     (Polynomial.cyclotomic (p ^ k * m) R).IsRoot μ ↔ IsPrimitiveRoot μ m :=
   by
+  letI : Algebra (ZMod p) R := ZMod.algebra _ _
   rcases k.eq_zero_or_pos with (rfl | hk)
   · rw [pow_zero, one_mul, is_root_cyclotomic_iff]
   refine' ⟨fun h => _, fun h => _⟩

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

@@ -37,6 +37,7 @@ We gather results relating cyclotomic polynomials and `expand`.
 
 namespace Polynomial
 
+#print Polynomial.cyclotomic_expand_eq_cyclotomic_mul /-
 /-- If `p` is a prime such that `¬ p ∣ n`, then
 `expand R p (cyclotomic n R) = (cyclotomic (n * p) R) * (cyclotomic n R)`. -/
 @[simp]
@@ -82,7 +83,9 @@ theorem cyclotomic_expand_eq_cyclotomic_mul {p n : ℕ} (hp : Nat.Prime p) (hdiv
       Nat.totient_mul ((Nat.Prime.coprime_iff_not_dvd hp).2 hdiv), Nat.totient_prime hp,
       mul_comm (p - 1), ← Nat.mul_succ, Nat.sub_one, Nat.succ_pred_eq_of_pos hp.pos]
 #align polynomial.cyclotomic_expand_eq_cyclotomic_mul Polynomial.cyclotomic_expand_eq_cyclotomic_mul
+-/
 
+#print Polynomial.cyclotomic_expand_eq_cyclotomic /-
 /-- If `p` is a prime such that `p ∣ n`, then
 `expand R p (cyclotomic n R) = cyclotomic (p * n) R`. -/
 @[simp]
@@ -109,7 +112,9 @@ theorem cyclotomic_expand_eq_cyclotomic {p n : ℕ} (hp : Nat.Prime p) (hdiv : p
     rw [nat_degree_expand, nat_degree_cyclotomic, nat_degree_cyclotomic, mul_comm n,
       Nat.totient_mul_of_prime_of_dvd hp hdiv, mul_comm]
 #align polynomial.cyclotomic_expand_eq_cyclotomic Polynomial.cyclotomic_expand_eq_cyclotomic
+-/
 
+#print Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow /-
 /-- If the `p ^ n`th cyclotomic polynomial is irreducible, so is the `p ^ m`th, for `m ≤ n`. -/
 theorem cyclotomic_irreducible_pow_of_irreducible_pow {p : ℕ} (hp : Nat.Prime p) {R} [CommRing R]
     [IsDomain R] {n m : ℕ} (hmn : m ≤ n) (h : Irreducible (cyclotomic (p ^ n) R)) :
@@ -124,16 +129,20 @@ theorem cyclotomic_irreducible_pow_of_irreducible_pow {p : ℕ} (hp : Nat.Prime
   rw [Nat.add_succ, pow_succ', ← cyclotomic_expand_eq_cyclotomic hp <| dvd_pow_self p this] at h 
   exact hk (by linarith) (of_irreducible_expand hp.ne_zero h)
 #align polynomial.cyclotomic_irreducible_pow_of_irreducible_pow Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow
+-/
 
+#print Polynomial.cyclotomic_irreducible_of_irreducible_pow /-
 /-- If `irreducible (cyclotomic (p ^ n) R)` then `irreducible (cyclotomic p R).` -/
 theorem cyclotomic_irreducible_of_irreducible_pow {p : ℕ} (hp : Nat.Prime p) {R} [CommRing R]
     [IsDomain R] {n : ℕ} (hn : n ≠ 0) (h : Irreducible (cyclotomic (p ^ n) R)) :
     Irreducible (cyclotomic p R) :=
   pow_one p ▸ cyclotomic_irreducible_pow_of_irreducible_pow hp hn.bot_lt h
 #align polynomial.cyclotomic_irreducible_of_irreducible_pow Polynomial.cyclotomic_irreducible_of_irreducible_pow
+-/
 
 section CharP
 
+#print Polynomial.cyclotomic_mul_prime_eq_pow_of_not_dvd /-
 /-- If `R` is of characteristic `p` and `¬p ∣ n`, then
 `cyclotomic (n * p) R = (cyclotomic n R) ^ (p - 1)`. -/
 theorem cyclotomic_mul_prime_eq_pow_of_not_dvd (R : Type _) {p n : ℕ} [hp : Fact (Nat.Prime p)]
@@ -148,7 +157,9 @@ theorem cyclotomic_mul_prime_eq_pow_of_not_dvd (R : Type _) {p n : ℕ} [hp : Fa
   rw [← map_expand, cyclotomic_expand_eq_cyclotomic_mul hp.out hn, Polynomial.map_mul,
     map_cyclotomic, map_cyclotomic]
 #align polynomial.cyclotomic_mul_prime_eq_pow_of_not_dvd Polynomial.cyclotomic_mul_prime_eq_pow_of_not_dvd
+-/
 
+#print Polynomial.cyclotomic_mul_prime_dvd_eq_pow /-
 /-- If `R` is of characteristic `p` and `p ∣ n`, then
 `cyclotomic (n * p) R = (cyclotomic n R) ^ p`. -/
 theorem cyclotomic_mul_prime_dvd_eq_pow (R : Type _) {p n : ℕ} [hp : Fact (Nat.Prime p)] [Ring R]
@@ -160,7 +171,9 @@ theorem cyclotomic_mul_prime_dvd_eq_pow (R : Type _) {p n : ℕ} [hp : Fact (Nat
   rw [← ZMod.expand_card, ← map_cyclotomic_int n, ← map_expand,
     cyclotomic_expand_eq_cyclotomic hp.out hn, map_cyclotomic, mul_comm]
 #align polynomial.cyclotomic_mul_prime_dvd_eq_pow Polynomial.cyclotomic_mul_prime_dvd_eq_pow
+-/
 
+#print Polynomial.cyclotomic_mul_prime_pow_eq /-
 /-- If `R` is of characteristic `p` and `¬p ∣ m`, then
 `cyclotomic (p ^ k * m) R = (cyclotomic m R) ^ (p ^ k - p ^ (k - 1))`. -/
 theorem cyclotomic_mul_prime_pow_eq (R : Type _) {p m : ℕ} [Fact (Nat.Prime p)] [Ring R] [CharP R p]
@@ -176,7 +189,9 @@ theorem cyclotomic_mul_prime_pow_eq (R : Type _) {p m : ℕ} [Fact (Nat.Prime p)
     simp only [tsub_zero, Nat.succ_sub_succ_eq_sub]
     rw [Nat.mul_sub_right_distrib, mul_comm, pow_succ']
 #align polynomial.cyclotomic_mul_prime_pow_eq Polynomial.cyclotomic_mul_prime_pow_eq
+-/
 
+#print Polynomial.isRoot_cyclotomic_prime_pow_mul_iff_of_charP /-
 /-- If `R` is of characteristic `p` and `¬p ∣ m`, then `ζ` is a root of `cyclotomic (p ^ k * m) R`
  if and only if it is a primitive `m`-th root of unity. -/
 theorem isRoot_cyclotomic_prime_pow_mul_iff_of_charP {m k p : ℕ} {R : Type _} [CommRing R]
@@ -195,6 +210,7 @@ theorem isRoot_cyclotomic_prime_pow_mul_iff_of_charP {m k p : ℕ} {R : Type _}
     simp only [tsub_pos_iff_lt]
     apply pow_strictMono_right hp.out.one_lt (Nat.pred_lt hk.ne')
 #align polynomial.is_root_cyclotomic_prime_pow_mul_iff_of_char_p Polynomial.isRoot_cyclotomic_prime_pow_mul_iff_of_charP
+-/
 
 end CharP
 

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.expand
-! leanprover-community/mathlib commit 5bfbcca0a7ffdd21cf1682e59106d6c942434a32
+! leanprover-community/mathlib commit 2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
 ! 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.Cyclotomic.Roots
 /-!
 # Cyclotomic polynomials and `expand`.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We gather results relating cyclotomic polynomials and `expand`.
 
 ## Main results

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

@@ -118,7 +118,7 @@ theorem cyclotomic_irreducible_pow_of_irreducible_pow {p : ℕ} (hp : Nat.Prime
   induction' k with k hk
   · simpa using h
   have : m + k ≠ 0 := (add_pos_of_pos_of_nonneg hm k.zero_le).ne'
-  rw [Nat.add_succ, pow_succ', ← cyclotomic_expand_eq_cyclotomic hp <| dvd_pow_self p this] at h
+  rw [Nat.add_succ, pow_succ', ← cyclotomic_expand_eq_cyclotomic hp <| dvd_pow_self p this] at h 
   exact hk (by linarith) (of_irreducible_expand hp.ne_zero h)
 #align polynomial.cyclotomic_irreducible_pow_of_irreducible_pow Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow
 
@@ -183,10 +183,10 @@ theorem isRoot_cyclotomic_prime_pow_mul_iff_of_charP {m k p : ℕ} {R : Type _}
   rcases k.eq_zero_or_pos with (rfl | hk)
   · rw [pow_zero, one_mul, is_root_cyclotomic_iff]
   refine' ⟨fun h => _, fun h => _⟩
-  · rw [is_root.def, cyclotomic_mul_prime_pow_eq R (NeZero.not_char_dvd R p m) hk, eval_pow] at h
+  · rw [is_root.def, cyclotomic_mul_prime_pow_eq R (NeZero.not_char_dvd R p m) hk, eval_pow] at h 
     replace h := pow_eq_zero h
-    rwa [← is_root.def, is_root_cyclotomic_iff] at h
-  · rw [← is_root_cyclotomic_iff, is_root.def] at h
+    rwa [← is_root.def, is_root_cyclotomic_iff] at h 
+  · rw [← is_root_cyclotomic_iff, is_root.def] at h 
     rw [cyclotomic_mul_prime_pow_eq R (NeZero.not_char_dvd R p m) hk, is_root.def, eval_pow, h,
       zero_pow]
     simp only [tsub_pos_iff_lt]

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

A PR analogous to #12338: reformatting proofs following the multiple goals linter of #12339.

@@ -156,9 +156,9 @@ theorem cyclotomic_mul_prime_pow_eq (R : Type*) {p m : ℕ} [Fact (Nat.Prime p)]
     have hdiv : p ∣ p ^ a.succ * m := ⟨p ^ a * m, by rw [← mul_assoc, pow_succ']⟩
     rw [pow_succ', mul_assoc, mul_comm, cyclotomic_mul_prime_dvd_eq_pow R hdiv,
       cyclotomic_mul_prime_pow_eq _ _ a.succ_pos, ← pow_mul]
-    congr 1
-    simp only [tsub_zero, Nat.succ_sub_succ_eq_sub]
-    rwa [Nat.mul_sub_right_distrib, mul_comm, pow_succ]
+    · simp only [tsub_zero, Nat.succ_sub_succ_eq_sub]
+      rw [Nat.mul_sub_right_distrib, mul_comm, pow_succ]
+    · assumption
 #align polynomial.cyclotomic_mul_prime_pow_eq Polynomial.cyclotomic_mul_prime_pow_eq
 
 /-- If `R` is of characteristic `p` and `¬p ∣ m`, then `ζ` is a root of `cyclotomic (p ^ k * m) R`

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

@@ -55,14 +55,14 @@ theorem cyclotomic_expand_eq_cyclotomic_mul {p n : ℕ} (hp : Nat.Prime p) (hdiv
       have hprim := Complex.isPrimitiveRoot_exp _ hpos.ne'
       rw [cyclotomic_eq_minpoly_rat hprim hpos]
       refine' minpoly.dvd ℚ _ _
-      rw [aeval_def, ← eval_map, map_expand, map_cyclotomic, expand_eval, ← IsRoot.definition,
+      rw [aeval_def, ← eval_map, map_expand, map_cyclotomic, expand_eval, ← IsRoot.def,
         @isRoot_cyclotomic_iff]
       convert IsPrimitiveRoot.pow_of_dvd hprim hp.ne_zero (dvd_mul_left p n)
       rw [Nat.mul_div_cancel _ (Nat.Prime.pos hp)]
     · have hprim := Complex.isPrimitiveRoot_exp _ hnpos.ne.symm
       rw [cyclotomic_eq_minpoly_rat hprim hnpos]
       refine' minpoly.dvd ℚ _ _
-      rw [aeval_def, ← eval_map, map_expand, expand_eval, ← IsRoot.definition, ←
+      rw [aeval_def, ← eval_map, map_expand, expand_eval, ← IsRoot.def, ←
         cyclotomic_eq_minpoly_rat hprim hnpos, map_cyclotomic, @isRoot_cyclotomic_iff]
       exact IsPrimitiveRoot.pow_of_prime hprim hp hdiv
   · rw [natDegree_expand, natDegree_cyclotomic,
@@ -88,7 +88,7 @@ theorem cyclotomic_expand_eq_cyclotomic {p n : ℕ} (hp : Nat.Prime p) (hdiv : p
     have hprim := Complex.isPrimitiveRoot_exp _ hpos.ne.symm
     rw [cyclotomic_eq_minpoly hprim hpos]
     refine' minpoly.isIntegrallyClosed_dvd (hprim.isIntegral hpos) _
-    rw [aeval_def, ← eval_map, map_expand, map_cyclotomic, expand_eval, ← IsRoot.definition,
+    rw [aeval_def, ← eval_map, map_expand, map_cyclotomic, expand_eval, ← IsRoot.def,
       @isRoot_cyclotomic_iff]
     · convert IsPrimitiveRoot.pow_of_dvd hprim hp.ne_zero (dvd_mul_left p n)
       rw [Nat.mul_div_cancel _ hp.pos]
@@ -169,12 +169,12 @@ theorem isRoot_cyclotomic_prime_pow_mul_iff_of_charP {m k p : ℕ} {R : Type*} [
   rcases k.eq_zero_or_pos with (rfl | hk)
   · rw [pow_zero, one_mul, isRoot_cyclotomic_iff]
   refine' ⟨fun h => _, fun h => _⟩
-  · rw [IsRoot.definition, cyclotomic_mul_prime_pow_eq R (NeZero.not_char_dvd R p m) hk, eval_pow]
+  · rw [IsRoot.def, cyclotomic_mul_prime_pow_eq R (NeZero.not_char_dvd R p m) hk, eval_pow]
       at h
     replace h := pow_eq_zero h
-    rwa [← IsRoot.definition, isRoot_cyclotomic_iff] at h
-  · rw [← isRoot_cyclotomic_iff, IsRoot.definition] at h
-    rw [cyclotomic_mul_prime_pow_eq R (NeZero.not_char_dvd R p m) hk, IsRoot.definition, eval_pow,
+    rwa [← IsRoot.def, isRoot_cyclotomic_iff] at h
+  · rw [← isRoot_cyclotomic_iff, IsRoot.def] at h
+    rw [cyclotomic_mul_prime_pow_eq R (NeZero.not_char_dvd R p m) hk, IsRoot.def, eval_pow,
       h, zero_pow]
     exact Nat.sub_ne_zero_of_lt $ pow_right_strictMono hp.out.one_lt $ Nat.pred_lt hk.ne'
 #align polynomial.is_root_cyclotomic_prime_pow_mul_iff_of_char_p Polynomial.isRoot_cyclotomic_prime_pow_mul_iff_of_charP

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

• pow_succ and pow_succ' have switched their meanings.
• Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
• In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
• the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

@@ -106,7 +106,7 @@ theorem cyclotomic_irreducible_pow_of_irreducible_pow {p : ℕ} (hp : Nat.Prime
   induction' k with k hk
   · simpa using h
   have : m + k ≠ 0 := (add_pos_of_pos_of_nonneg hm k.zero_le).ne'
-  rw [Nat.add_succ, pow_succ', ← cyclotomic_expand_eq_cyclotomic hp <| dvd_pow_self p this] at h
+  rw [Nat.add_succ, pow_succ, ← cyclotomic_expand_eq_cyclotomic hp <| dvd_pow_self p this] at h
   exact hk (by omega) (of_irreducible_expand hp.ne_zero h)
 #align polynomial.cyclotomic_irreducible_pow_of_irreducible_pow Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow
 
@@ -128,7 +128,7 @@ theorem cyclotomic_mul_prime_eq_pow_of_not_dvd (R : Type*) {p n : ℕ} [hp : Fac
     rw [← map_cyclotomic _ (algebraMap (ZMod p) R), ← map_cyclotomic _ (algebraMap (ZMod p) R),
       this, Polynomial.map_pow]
   apply mul_right_injective₀ (cyclotomic_ne_zero n <| ZMod p); dsimp
-  rw [← pow_succ, tsub_add_cancel_of_le hp.out.one_lt.le, mul_comm, ← ZMod.expand_card]
+  rw [← pow_succ', tsub_add_cancel_of_le hp.out.one_lt.le, mul_comm, ← ZMod.expand_card]
   conv_rhs => rw [← map_cyclotomic_int]
   rw [← map_expand, cyclotomic_expand_eq_cyclotomic_mul hp.out hn, Polynomial.map_mul,
     map_cyclotomic, map_cyclotomic]
@@ -153,12 +153,12 @@ theorem cyclotomic_mul_prime_pow_eq (R : Type*) {p m : ℕ} [Fact (Nat.Prime p)]
   | 1, _ => by
     rw [pow_one, Nat.sub_self, pow_zero, mul_comm, cyclotomic_mul_prime_eq_pow_of_not_dvd R hm]
   | a + 2, _ => by
-    have hdiv : p ∣ p ^ a.succ * m := ⟨p ^ a * m, by rw [← mul_assoc, pow_succ]⟩
-    rw [pow_succ, mul_assoc, mul_comm, cyclotomic_mul_prime_dvd_eq_pow R hdiv,
+    have hdiv : p ∣ p ^ a.succ * m := ⟨p ^ a * m, by rw [← mul_assoc, pow_succ']⟩
+    rw [pow_succ', mul_assoc, mul_comm, cyclotomic_mul_prime_dvd_eq_pow R hdiv,
       cyclotomic_mul_prime_pow_eq _ _ a.succ_pos, ← pow_mul]
     congr 1
     simp only [tsub_zero, Nat.succ_sub_succ_eq_sub]
-    rwa [Nat.mul_sub_right_distrib, mul_comm, pow_succ']
+    rwa [Nat.mul_sub_right_distrib, mul_comm, pow_succ]
 #align polynomial.cyclotomic_mul_prime_pow_eq Polynomial.cyclotomic_mul_prime_pow_eq
 
 /-- If `R` is of characteristic `p` and `¬p ∣ m`, then `ζ` is a root of `cyclotomic (p ^ k * m) R`

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

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

@@ -55,14 +55,14 @@ theorem cyclotomic_expand_eq_cyclotomic_mul {p n : ℕ} (hp : Nat.Prime p) (hdiv
       have hprim := Complex.isPrimitiveRoot_exp _ hpos.ne'
       rw [cyclotomic_eq_minpoly_rat hprim hpos]
       refine' minpoly.dvd ℚ _ _
-      rw [aeval_def, ← eval_map, map_expand, map_cyclotomic, expand_eval, ← IsRoot.def,
+      rw [aeval_def, ← eval_map, map_expand, map_cyclotomic, expand_eval, ← IsRoot.definition,
         @isRoot_cyclotomic_iff]
       convert IsPrimitiveRoot.pow_of_dvd hprim hp.ne_zero (dvd_mul_left p n)
       rw [Nat.mul_div_cancel _ (Nat.Prime.pos hp)]
     · have hprim := Complex.isPrimitiveRoot_exp _ hnpos.ne.symm
       rw [cyclotomic_eq_minpoly_rat hprim hnpos]
       refine' minpoly.dvd ℚ _ _
-      rw [aeval_def, ← eval_map, map_expand, expand_eval, ← IsRoot.def, ←
+      rw [aeval_def, ← eval_map, map_expand, expand_eval, ← IsRoot.definition, ←
         cyclotomic_eq_minpoly_rat hprim hnpos, map_cyclotomic, @isRoot_cyclotomic_iff]
       exact IsPrimitiveRoot.pow_of_prime hprim hp hdiv
   · rw [natDegree_expand, natDegree_cyclotomic,
@@ -88,7 +88,7 @@ theorem cyclotomic_expand_eq_cyclotomic {p n : ℕ} (hp : Nat.Prime p) (hdiv : p
     have hprim := Complex.isPrimitiveRoot_exp _ hpos.ne.symm
     rw [cyclotomic_eq_minpoly hprim hpos]
     refine' minpoly.isIntegrallyClosed_dvd (hprim.isIntegral hpos) _
-    rw [aeval_def, ← eval_map, map_expand, map_cyclotomic, expand_eval, ← IsRoot.def,
+    rw [aeval_def, ← eval_map, map_expand, map_cyclotomic, expand_eval, ← IsRoot.definition,
       @isRoot_cyclotomic_iff]
     · convert IsPrimitiveRoot.pow_of_dvd hprim hp.ne_zero (dvd_mul_left p n)
       rw [Nat.mul_div_cancel _ hp.pos]
@@ -169,12 +169,13 @@ theorem isRoot_cyclotomic_prime_pow_mul_iff_of_charP {m k p : ℕ} {R : Type*} [
   rcases k.eq_zero_or_pos with (rfl | hk)
   · rw [pow_zero, one_mul, isRoot_cyclotomic_iff]
   refine' ⟨fun h => _, fun h => _⟩
-  · rw [IsRoot.def, cyclotomic_mul_prime_pow_eq R (NeZero.not_char_dvd R p m) hk, eval_pow] at h
+  · rw [IsRoot.definition, cyclotomic_mul_prime_pow_eq R (NeZero.not_char_dvd R p m) hk, eval_pow]
+      at h
     replace h := pow_eq_zero h
-    rwa [← IsRoot.def, isRoot_cyclotomic_iff] at h
-  · rw [← isRoot_cyclotomic_iff, IsRoot.def] at h
-    rw [cyclotomic_mul_prime_pow_eq R (NeZero.not_char_dvd R p m) hk, IsRoot.def, eval_pow, h,
-      zero_pow]
+    rwa [← IsRoot.definition, isRoot_cyclotomic_iff] at h
+  · rw [← isRoot_cyclotomic_iff, IsRoot.definition] at h
+    rw [cyclotomic_mul_prime_pow_eq R (NeZero.not_char_dvd R p m) hk, IsRoot.definition, eval_pow,
+      h, zero_pow]
     exact Nat.sub_ne_zero_of_lt $ pow_right_strictMono hp.out.one_lt $ Nat.pred_lt hk.ne'
 #align polynomial.is_root_cyclotomic_prime_pow_mul_iff_of_char_p Polynomial.isRoot_cyclotomic_prime_pow_mul_iff_of_charP
 

I ran tryAtEachStep on all files under Mathlib to find all locations where omega succeeds. For each that was a linarith without an only, I tried replacing it with omega, and I verified that elaboration time got smaller. (In almost all cases, there was a noticeable speedup.) I also replaced some slow aesops along the way.

@@ -107,7 +107,7 @@ theorem cyclotomic_irreducible_pow_of_irreducible_pow {p : ℕ} (hp : Nat.Prime
   · simpa using h
   have : m + k ≠ 0 := (add_pos_of_pos_of_nonneg hm k.zero_le).ne'
   rw [Nat.add_succ, pow_succ', ← cyclotomic_expand_eq_cyclotomic hp <| dvd_pow_self p this] at h
-  exact hk (by linarith) (of_irreducible_expand hp.ne_zero h)
+  exact hk (by omega) (of_irreducible_expand hp.ne_zero h)
 #align polynomial.cyclotomic_irreducible_pow_of_irreducible_pow Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow
 
 /-- If `Irreducible (cyclotomic (p ^ n) R)` then `Irreducible (cyclotomic p R).` -/

Moving these to separate files should make typeclass synthesis less expensive. Additionally two of them are quite long and this shrinks them slightly.

This handles:

• Submonoid
• Subgroup
• Subsemiring
• Subring
• Subfield
• Submodule
• Subalgebra

This also moves Units.posSubgroup into its own file.

The copyright headers are from:

• https://github.com/leanprover-community/mathlib/pull/6489
• https://github.com/leanprover-community/mathlib/pull/8466

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -42,7 +42,7 @@ theorem cyclotomic_expand_eq_cyclotomic_mul {p n : ℕ} (hp : Nat.Prime p) (hdiv
   suffices expand ℤ p (cyclotomic n ℤ) = cyclotomic (n * p) ℤ * cyclotomic n ℤ by
     rw [← map_cyclotomic_int, ← map_expand, this, Polynomial.map_mul, map_cyclotomic_int,
       map_cyclotomic]
-  refine' eq_of_monic_of_dvd_of_natDegree_le ((cyclotomic.monic _ ℤ).mul (cyclotomic.monic _ _))
+  refine' eq_of_monic_of_dvd_of_natDegree_le ((cyclotomic.monic _ ℤ).mul (cyclotomic.monic _ ℤ))
     ((cyclotomic.monic n ℤ).expand hp.pos) _ _
   · refine' (IsPrimitive.Int.dvd_iff_map_cast_dvd_map_cast _ _
       (IsPrimitive.mul (cyclotomic.isPrimitive (n * p) ℤ) (cyclotomic.isPrimitive n ℤ))
@@ -54,14 +54,14 @@ theorem cyclotomic_expand_eq_cyclotomic_mul {p n : ℕ} (hp : Nat.Prime p) (hdiv
     · have hpos : 0 < n * p := mul_pos hnpos hp.pos
       have hprim := Complex.isPrimitiveRoot_exp _ hpos.ne'
       rw [cyclotomic_eq_minpoly_rat hprim hpos]
-      refine' @minpoly.dvd ℚ ℂ _ _ algebraRat _ _ _
+      refine' minpoly.dvd ℚ _ _
       rw [aeval_def, ← eval_map, map_expand, map_cyclotomic, expand_eval, ← IsRoot.def,
         @isRoot_cyclotomic_iff]
       convert IsPrimitiveRoot.pow_of_dvd hprim hp.ne_zero (dvd_mul_left p n)
       rw [Nat.mul_div_cancel _ (Nat.Prime.pos hp)]
     · have hprim := Complex.isPrimitiveRoot_exp _ hnpos.ne.symm
       rw [cyclotomic_eq_minpoly_rat hprim hnpos]
-      refine' @minpoly.dvd ℚ ℂ _ _ algebraRat _ _ _
+      refine' minpoly.dvd ℚ _ _
       rw [aeval_def, ← eval_map, map_expand, expand_eval, ← IsRoot.def, ←
         cyclotomic_eq_minpoly_rat hprim hnpos, map_cyclotomic, @isRoot_cyclotomic_iff]
       exact IsPrimitiveRoot.pow_of_prime hprim hp hdiv
@@ -82,7 +82,7 @@ theorem cyclotomic_expand_eq_cyclotomic {p n : ℕ} (hp : Nat.Prime p) (hdiv : p
   haveI := NeZero.of_pos hzero
   suffices expand ℤ p (cyclotomic n ℤ) = cyclotomic (n * p) ℤ by
     rw [← map_cyclotomic_int, ← map_expand, this, map_cyclotomic_int]
-  refine' eq_of_monic_of_dvd_of_natDegree_le (cyclotomic.monic _ _)
+  refine' eq_of_monic_of_dvd_of_natDegree_le (cyclotomic.monic _ ℤ)
     ((cyclotomic.monic n ℤ).expand hp.pos) _ _
   · have hpos := Nat.mul_pos hzero hp.pos
     have hprim := Complex.isPrimitiveRoot_exp _ hpos.ne.symm

Remove unnecessary "rw"s.

@@ -143,7 +143,7 @@ theorem cyclotomic_mul_prime_dvd_eq_pow (R : Type*) {p n : ℕ} [hp : Fact (Nat.
     rw [← map_cyclotomic _ (algebraMap (ZMod p) R), ← map_cyclotomic _ (algebraMap (ZMod p) R),
       this, Polynomial.map_pow]
   rw [← ZMod.expand_card, ← map_cyclotomic_int n, ← map_expand,
-    cyclotomic_expand_eq_cyclotomic hp.out hn, map_cyclotomic, mul_comm]
+    cyclotomic_expand_eq_cyclotomic hp.out hn, map_cyclotomic]
 #align polynomial.cyclotomic_mul_prime_dvd_eq_pow Polynomial.cyclotomic_mul_prime_dvd_eq_pow
 
 /-- If `R` is of characteristic `p` and `¬p ∣ m`, then

This involves moving lemmas from Algebra.GroupPower.Ring to Algebra.GroupWithZero.Basic and changing some 0 < n assumptions to n ≠ 0.

From LeanAPAP

@@ -175,8 +175,7 @@ theorem isRoot_cyclotomic_prime_pow_mul_iff_of_charP {m k p : ℕ} {R : Type*} [
   · rw [← isRoot_cyclotomic_iff, IsRoot.def] at h
     rw [cyclotomic_mul_prime_pow_eq R (NeZero.not_char_dvd R p m) hk, IsRoot.def, eval_pow, h,
       zero_pow]
-    simp only [tsub_pos_iff_lt]
-    apply pow_right_strictMono hp.out.one_lt (Nat.pred_lt hk.ne')
+    exact Nat.sub_ne_zero_of_lt $ pow_right_strictMono hp.out.one_lt $ Nat.pred_lt hk.ne'
 #align polynomial.is_root_cyclotomic_prime_pow_mul_iff_of_char_p Polynomial.isRoot_cyclotomic_prime_pow_mul_iff_of_charP
 
 end CharP

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 -/
 import Mathlib.RingTheory.Polynomial.Cyclotomic.Roots
+import Mathlib.Data.ZMod.Algebra
 
 #align_import ring_theory.polynomial.cyclotomic.expand from "leanprover-community/mathlib"@"0723536a0522d24fc2f159a096fb3304bef77472"
 

The names for lemmas about monotonicity of (a ^ ·) and (· ^ n) were a mess. This PR tidies up everything related by following the naming convention for (a * ·) and (· * b). Namely, (a ^ ·) is pow_right and (· ^ n) is pow_left in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.

Renames

Algebra.GroupPower.Order

• pow_mono → pow_right_mono
• pow_le_pow → pow_le_pow_right
• pow_le_pow_of_le_left → pow_le_pow_left
• pow_lt_pow_of_lt_left → pow_lt_pow_left
• strictMonoOn_pow → pow_left_strictMonoOn
• pow_strictMono_right → pow_right_strictMono
• pow_lt_pow → pow_lt_pow_right
• pow_lt_pow_iff → pow_lt_pow_iff_right
• pow_le_pow_iff → pow_le_pow_iff_right
• self_lt_pow → lt_self_pow
• strictAnti_pow → pow_right_strictAnti
• pow_lt_pow_iff_of_lt_one → pow_lt_pow_iff_right_of_lt_one
• pow_lt_pow_of_lt_one → pow_lt_pow_right_of_lt_one
• lt_of_pow_lt_pow → lt_of_pow_lt_pow_left
• le_of_pow_le_pow → le_of_pow_le_pow_left
• pow_lt_pow₀ → pow_lt_pow_right₀

Algebra.GroupPower.CovariantClass

• pow_le_pow_of_le_left' → pow_le_pow_left'
• nsmul_le_nsmul_of_le_right → nsmul_le_nsmul_right
• pow_lt_pow' → pow_lt_pow_right'
• nsmul_lt_nsmul → nsmul_lt_nsmul_left
• pow_strictMono_left → pow_right_strictMono'
• nsmul_strictMono_right → nsmul_left_strictMono
• StrictMono.pow_right' → StrictMono.pow_const
• StrictMono.nsmul_left → StrictMono.const_nsmul
• pow_strictMono_right' → pow_left_strictMono
• nsmul_strictMono_left → nsmul_right_strictMono
• Monotone.pow_right → Monotone.pow_const
• Monotone.nsmul_left → Monotone.const_nsmul
• lt_of_pow_lt_pow' → lt_of_pow_lt_pow_left'
• lt_of_nsmul_lt_nsmul → lt_of_nsmul_lt_nsmul_right
• pow_le_pow' → pow_le_pow_right'
• nsmul_le_nsmul → nsmul_le_nsmul_left
• pow_le_pow_of_le_one' → pow_le_pow_right_of_le_one'
• nsmul_le_nsmul_of_nonpos → nsmul_le_nsmul_left_of_nonpos
• le_of_pow_le_pow' → le_of_pow_le_pow_left'
• le_of_nsmul_le_nsmul' → le_of_nsmul_le_nsmul_right'
• pow_le_pow_iff' → pow_le_pow_iff_right'
• nsmul_le_nsmul_iff → nsmul_le_nsmul_iff_left
• pow_lt_pow_iff' → pow_lt_pow_iff_right'
• nsmul_lt_nsmul_iff → nsmul_lt_nsmul_iff_left

Data.Nat.Pow

• Nat.pow_lt_pow_of_lt_left → Nat.pow_lt_pow_left
• Nat.pow_le_iff_le_left → Nat.pow_le_pow_iff_left
• Nat.pow_lt_iff_lt_left → Nat.pow_lt_pow_iff_left

Lemmas added

• pow_le_pow_iff_left
• pow_lt_pow_iff_left
• pow_right_injective
• pow_right_inj
• Nat.pow_le_pow_left to have the correct name since Nat.pow_le_pow_of_le_left is in Std.
• Nat.pow_le_pow_right to have the correct name since Nat.pow_le_pow_of_le_right is in Std.

Lemmas removed

• self_le_pow was a duplicate of le_self_pow.
• Nat.pow_lt_pow_of_lt_right is defeq to pow_lt_pow_right.
• Nat.pow_right_strictMono is defeq to pow_right_strictMono.
• Nat.pow_le_iff_le_right is defeq to pow_le_pow_iff_right.
• Nat.pow_lt_iff_lt_right is defeq to pow_lt_pow_iff_right.

Other changes

• A bunch of proofs have been golfed.
• Some lemma assumptions have been turned from 0 < n or 1 ≤ n to n ≠ 0.
• A few Nat lemmas have been protected.
• One docstring has been fixed.

@@ -175,7 +175,7 @@ theorem isRoot_cyclotomic_prime_pow_mul_iff_of_charP {m k p : ℕ} {R : Type*} [
     rw [cyclotomic_mul_prime_pow_eq R (NeZero.not_char_dvd R p m) hk, IsRoot.def, eval_pow, h,
       zero_pow]
     simp only [tsub_pos_iff_lt]
-    apply pow_strictMono_right hp.out.one_lt (Nat.pred_lt hk.ne')
+    apply pow_right_strictMono hp.out.one_lt (Nat.pred_lt hk.ne')
 #align polynomial.is_root_cyclotomic_prime_pow_mul_iff_of_char_p Polynomial.isRoot_cyclotomic_prime_pow_mul_iff_of_charP
 
 end CharP

This eliminates (fun a ↦ β) α in the type when applying a FunLike.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -80,7 +80,7 @@ theorem cyclotomic_expand_eq_cyclotomic {p n : ℕ} (hp : Nat.Prime p) (hdiv : p
   · simp
   haveI := NeZero.of_pos hzero
   suffices expand ℤ p (cyclotomic n ℤ) = cyclotomic (n * p) ℤ by
-    rw [← map_cyclotomic_int, ← map_expand, this, map_cyclotomic_int, map_cyclotomic]
+    rw [← map_cyclotomic_int, ← map_expand, this, map_cyclotomic_int]
   refine' eq_of_monic_of_dvd_of_natDegree_le (cyclotomic.monic _ _)
     ((cyclotomic.monic n ℤ).expand hp.pos) _ _
   · have hpos := Nat.mul_pos hzero hp.pos

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

This has nice performance benefits.

@@ -33,7 +33,7 @@ namespace Polynomial
 `expand R p (cyclotomic n R) = (cyclotomic (n * p) R) * (cyclotomic n R)`. -/
 @[simp]
 theorem cyclotomic_expand_eq_cyclotomic_mul {p n : ℕ} (hp : Nat.Prime p) (hdiv : ¬p ∣ n)
-    (R : Type _) [CommRing R] :
+    (R : Type*) [CommRing R] :
     expand R p (cyclotomic n R) = cyclotomic (n * p) R * cyclotomic n R := by
   rcases Nat.eq_zero_or_pos n with (rfl | hnpos)
   · simp
@@ -74,7 +74,7 @@ theorem cyclotomic_expand_eq_cyclotomic_mul {p n : ℕ} (hp : Nat.Prime p) (hdiv
 /-- If `p` is a prime such that `p ∣ n`, then
 `expand R p (cyclotomic n R) = cyclotomic (p * n) R`. -/
 @[simp]
-theorem cyclotomic_expand_eq_cyclotomic {p n : ℕ} (hp : Nat.Prime p) (hdiv : p ∣ n) (R : Type _)
+theorem cyclotomic_expand_eq_cyclotomic {p n : ℕ} (hp : Nat.Prime p) (hdiv : p ∣ n) (R : Type*)
     [CommRing R] : expand R p (cyclotomic n R) = cyclotomic (n * p) R := by
   rcases n.eq_zero_or_pos with (rfl | hzero)
   · simp
@@ -120,7 +120,7 @@ section CharP
 
 /-- If `R` is of characteristic `p` and `¬p ∣ n`, then
 `cyclotomic (n * p) R = (cyclotomic n R) ^ (p - 1)`. -/
-theorem cyclotomic_mul_prime_eq_pow_of_not_dvd (R : Type _) {p n : ℕ} [hp : Fact (Nat.Prime p)]
+theorem cyclotomic_mul_prime_eq_pow_of_not_dvd (R : Type*) {p n : ℕ} [hp : Fact (Nat.Prime p)]
     [Ring R] [CharP R p] (hn : ¬p ∣ n) : cyclotomic (n * p) R = cyclotomic n R ^ (p - 1) := by
   letI : Algebra (ZMod p) R := ZMod.algebra _ _
   suffices cyclotomic (n * p) (ZMod p) = cyclotomic n (ZMod p) ^ (p - 1) by
@@ -135,7 +135,7 @@ theorem cyclotomic_mul_prime_eq_pow_of_not_dvd (R : Type _) {p n : ℕ} [hp : Fa
 
 /-- If `R` is of characteristic `p` and `p ∣ n`, then
 `cyclotomic (n * p) R = (cyclotomic n R) ^ p`. -/
-theorem cyclotomic_mul_prime_dvd_eq_pow (R : Type _) {p n : ℕ} [hp : Fact (Nat.Prime p)] [Ring R]
+theorem cyclotomic_mul_prime_dvd_eq_pow (R : Type*) {p n : ℕ} [hp : Fact (Nat.Prime p)] [Ring R]
     [CharP R p] (hn : p ∣ n) : cyclotomic (n * p) R = cyclotomic n R ^ p := by
   letI : Algebra (ZMod p) R := ZMod.algebra _ _
   suffices cyclotomic (n * p) (ZMod p) = cyclotomic n (ZMod p) ^ p by
@@ -147,7 +147,7 @@ theorem cyclotomic_mul_prime_dvd_eq_pow (R : Type _) {p n : ℕ} [hp : Fact (Nat
 
 /-- If `R` is of characteristic `p` and `¬p ∣ m`, then
 `cyclotomic (p ^ k * m) R = (cyclotomic m R) ^ (p ^ k - p ^ (k - 1))`. -/
-theorem cyclotomic_mul_prime_pow_eq (R : Type _) {p m : ℕ} [Fact (Nat.Prime p)] [Ring R] [CharP R p]
+theorem cyclotomic_mul_prime_pow_eq (R : Type*) {p m : ℕ} [Fact (Nat.Prime p)] [Ring R] [CharP R p]
     (hm : ¬p ∣ m) : ∀ {k}, 0 < k → cyclotomic (p ^ k * m) R = cyclotomic m R ^ (p ^ k - p ^ (k - 1))
   | 1, _ => by
     rw [pow_one, Nat.sub_self, pow_zero, mul_comm, cyclotomic_mul_prime_eq_pow_of_not_dvd R hm]
@@ -162,7 +162,7 @@ theorem cyclotomic_mul_prime_pow_eq (R : Type _) {p m : ℕ} [Fact (Nat.Prime p)
 
 /-- If `R` is of characteristic `p` and `¬p ∣ m`, then `ζ` is a root of `cyclotomic (p ^ k * m) R`
  if and only if it is a primitive `m`-th root of unity. -/
-theorem isRoot_cyclotomic_prime_pow_mul_iff_of_charP {m k p : ℕ} {R : Type _} [CommRing R]
+theorem isRoot_cyclotomic_prime_pow_mul_iff_of_charP {m k p : ℕ} {R : Type*} [CommRing R]
     [IsDomain R] [hp : Fact (Nat.Prime p)] [hchar : CharP R p] {μ : R} [NeZero (m : R)] :
     (Polynomial.cyclotomic (p ^ k * m) R).IsRoot μ ↔ IsPrimitiveRoot μ m := by
   rcases k.eq_zero_or_pos with (rfl | hk)

• depends on: #5966

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

@@ -2,14 +2,11 @@
 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.expand
-! leanprover-community/mathlib commit 0723536a0522d24fc2f159a096fb3304bef77472
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.Polynomial.Cyclotomic.Roots
 
+#align_import ring_theory.polynomial.cyclotomic.expand from "leanprover-community/mathlib"@"0723536a0522d24fc2f159a096fb3304bef77472"
+
 /-!
 # Cyclotomic polynomials and `expand`.
 

@@ -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.expand
-! leanprover-community/mathlib commit 5bfbcca0a7ffdd21cf1682e59106d6c942434a32
+! leanprover-community/mathlib commit 0723536a0522d24fc2f159a096fb3304bef77472
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -125,6 +125,7 @@ section CharP
 `cyclotomic (n * p) R = (cyclotomic n R) ^ (p - 1)`. -/
 theorem cyclotomic_mul_prime_eq_pow_of_not_dvd (R : Type _) {p n : ℕ} [hp : Fact (Nat.Prime p)]
     [Ring R] [CharP R p] (hn : ¬p ∣ n) : cyclotomic (n * p) R = cyclotomic n R ^ (p - 1) := by
+  letI : Algebra (ZMod p) R := ZMod.algebra _ _
   suffices cyclotomic (n * p) (ZMod p) = cyclotomic n (ZMod p) ^ (p - 1) by
     rw [← map_cyclotomic _ (algebraMap (ZMod p) R), ← map_cyclotomic _ (algebraMap (ZMod p) R),
       this, Polynomial.map_pow]
@@ -139,6 +140,7 @@ theorem cyclotomic_mul_prime_eq_pow_of_not_dvd (R : Type _) {p n : ℕ} [hp : Fa
 `cyclotomic (n * p) R = (cyclotomic n R) ^ p`. -/
 theorem cyclotomic_mul_prime_dvd_eq_pow (R : Type _) {p n : ℕ} [hp : Fact (Nat.Prime p)] [Ring R]
     [CharP R p] (hn : p ∣ n) : cyclotomic (n * p) R = cyclotomic n R ^ p := by
+  letI : Algebra (ZMod p) R := ZMod.algebra _ _
   suffices cyclotomic (n * p) (ZMod p) = cyclotomic n (ZMod p) ^ p by
     rw [← map_cyclotomic _ (algebraMap (ZMod p) R), ← map_cyclotomic _ (algebraMap (ZMod p) R),
       this, Polynomial.map_pow]