ring_theory.polynomial.cyclotomic.eval ⟷ Mathlib.RingTheory.Polynomial.Cyclotomic.Eval

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

@@ -200,7 +200,7 @@ theorem eval_one_cyclotomic_not_prime_pow {R : Type _} [Ring R] {n : ℕ}
   obtain ⟨t, ht⟩ := hpe
   rw [Finset.prod_singleton, ht, mul_left_comm, mul_comm, ← mul_assoc, mul_assoc] at this
   have : (p ^ padicValNat p n * p : ℤ) ∣ n := ⟨_, this⟩
-  simp only [← pow_succ', ← Int.natAbs_dvd_natAbs, Int.natAbs_ofNat, Int.natAbs_pow] at this
+  simp only [← pow_succ, ← Int.natAbs_dvd_natAbs, Int.natAbs_ofNat, Int.natAbs_pow] at this
   exact pow_succ_padicValNat_not_dvd hn'.ne' this
   · rintro x - y - hxy
     apply Nat.succ_injective

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

@@ -70,16 +70,16 @@ private theorem cyclotomic_neg_one_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrdered
     Int.cast_pos]
   suffices 0 < eval (↑(-1 : ℤ)) (cyclotomic n ℝ)
     by
-    rw [← map_cyclotomic_int n ℝ, eval_int_cast_map, Int.coe_castRingHom] at this 
+    rw [← map_cyclotomic_int n ℝ, eval_int_cast_map, Int.coe_castRingHom] at this
     exact_mod_cast this
   simp only [Int.cast_one, Int.cast_neg]
   have h0 := cyclotomic_coeff_zero ℝ hn.le
-  rw [coeff_zero_eq_eval_zero] at h0 
+  rw [coeff_zero_eq_eval_zero] at h0
   by_contra! hx
   have := intermediate_value_univ (-1) 0 (cyclotomic n ℝ).Continuous
   obtain ⟨y, hy : is_root _ y⟩ := this (show (0 : ℝ) ∈ Set.Icc _ _ by simpa [h0] using hx)
-  rw [is_root_cyclotomic_iff] at hy 
-  rw [hy.eq_order_of] at hn 
+  rw [is_root_cyclotomic_iff] at hy
+  rw [hy.eq_order_of] at hn
   exact hn.not_le LinearOrderedRing.orderOf_le_two
 
 #print Polynomial.cyclotomic_pos /-
@@ -89,18 +89,18 @@ theorem cyclotomic_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrderedCommRing R] (x :
   induction' n using Nat.strong_induction_on with n ih
   have hn' : 0 < n := pos_of_gt hn
   have hn'' : 1 < n := one_lt_two.trans hn
-  dsimp at ih 
+  dsimp at ih
   have := prod_cyclotomic_eq_geom_sum hn' R
-  apply_fun eval x at this 
+  apply_fun eval x at this
   rw [← cons_self_proper_divisors hn'.ne', Finset.erase_cons_of_ne _ hn''.ne', Finset.prod_cons,
-    eval_mul, eval_geom_sum] at this 
+    eval_mul, eval_geom_sum] at this
   rcases lt_trichotomy 0 (∑ i in Finset.range n, x ^ i) with (h | h | h)
   · apply pos_of_mul_pos_left
     · rwa [this]
     rw [eval_prod]
     refine' Finset.prod_nonneg fun i hi => _
-    simp only [Finset.mem_erase, mem_proper_divisors] at hi 
-    rw [geom_sum_pos_iff hn'.ne'] at h 
+    simp only [Finset.mem_erase, mem_proper_divisors] at hi
+    rw [geom_sum_pos_iff hn'.ne'] at h
     cases' h with hk hx
     · refine' (ih _ hi.2.2 (Nat.two_lt_of_ne _ hi.1 _)).le <;> rintro rfl
       · exact hn'.ne' (zero_dvd_iff.mp hi.2.1)
@@ -110,11 +110,11 @@ theorem cyclotomic_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrderedCommRing R] (x :
       refine' (ih _ hi.2.2 (Nat.two_lt_of_ne _ hi.1 hk)).le
       rintro rfl
       exact hn'.ne' <| zero_dvd_iff.mp hi.2.1
-  · rw [eq_comm, geom_sum_eq_zero_iff_neg_one hn'.ne'] at h 
+  · rw [eq_comm, geom_sum_eq_zero_iff_neg_one hn'.ne'] at h
     exact h.1.symm ▸ cyclotomic_neg_one_pos hn
   · apply pos_of_mul_neg_left
     · rwa [this]
-    rw [geom_sum_neg_iff hn'.ne'] at h 
+    rw [geom_sum_neg_iff hn'.ne'] at h
     have h2 : 2 ∈ n.proper_divisors.erase 1 :=
       by
       rw [Finset.mem_erase, mem_proper_divisors]
@@ -122,10 +122,10 @@ theorem cyclotomic_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrderedCommRing R] (x :
     rw [eval_prod, ← Finset.prod_erase_mul _ _ h2]
     apply mul_nonpos_of_nonneg_of_nonpos
     · refine' Finset.prod_nonneg fun i hi => le_of_lt _
-      simp only [Finset.mem_erase, mem_proper_divisors] at hi 
+      simp only [Finset.mem_erase, mem_proper_divisors] at hi
       refine' ih _ hi.2.2.2 (Nat.two_lt_of_ne _ hi.2.1 hi.1)
       rintro rfl
-      rw [zero_dvd_iff] at hi 
+      rw [zero_dvd_iff] at hi
       exact hn'.ne' hi.2.2.1
     · simpa only [eval_X, eval_one, cyclotomic_two, eval_add] using h.right.le
 #align polynomial.cyclotomic_pos Polynomial.cyclotomic_pos
@@ -186,21 +186,21 @@ theorem eval_one_cyclotomic_not_prime_pow {R : Type _} [Ring R] {n : ℕ}
     apply Finset.dvd_prod_of_mem
     simp [hn'.ne', hn.ne']
   have := prod_cyclotomic_eq_geom_sum hn' ℤ
-  apply_fun eval 1 at this 
+  apply_fun eval 1 at this
   rw [eval_geom_sum, one_geom_sum, eval_prod, eq_comm, ←
-    Finset.prod_sdiff <| @range_pow_padicValNat_subset_divisors' p _ _, Finset.prod_image] at this 
-  simp_rw [eval_one_cyclotomic_prime_pow, Finset.prod_const, Finset.card_range, mul_comm] at this 
-  rw [← Finset.prod_sdiff <| show {n} ⊆ _ from _] at this 
+    Finset.prod_sdiff <| @range_pow_padicValNat_subset_divisors' p _ _, Finset.prod_image] at this
+  simp_rw [eval_one_cyclotomic_prime_pow, Finset.prod_const, Finset.card_range, mul_comm] at this
+  rw [← Finset.prod_sdiff <| show {n} ⊆ _ from _] at this
   any_goals infer_instance
   swap
   · simp only [singleton_subset_iff, mem_sdiff, mem_erase, Ne.def, mem_divisors, dvd_refl,
       true_and_iff, mem_image, mem_range, exists_prop, not_exists, not_and]
     exact ⟨⟨hn.ne', hn'.ne'⟩, fun t _ => h hp _⟩
-  rw [← Int.natAbs_ofNat p, Int.natAbs_dvd_natAbs] at hpe 
+  rw [← Int.natAbs_ofNat p, Int.natAbs_dvd_natAbs] at hpe
   obtain ⟨t, ht⟩ := hpe
-  rw [Finset.prod_singleton, ht, mul_left_comm, mul_comm, ← mul_assoc, mul_assoc] at this 
+  rw [Finset.prod_singleton, ht, mul_left_comm, mul_comm, ← mul_assoc, mul_assoc] at this
   have : (p ^ padicValNat p n * p : ℤ) ∣ n := ⟨_, this⟩
-  simp only [← pow_succ', ← Int.natAbs_dvd_natAbs, Int.natAbs_ofNat, Int.natAbs_pow] at this 
+  simp only [← pow_succ', ← Int.natAbs_dvd_natAbs, Int.natAbs_ofNat, Int.natAbs_pow] at this
   exact pow_succ_padicValNat_not_dvd hn'.ne' this
   · rintro x - y - hxy
     apply Nat.succ_injective
@@ -217,7 +217,7 @@ theorem sub_one_pow_totient_lt_cyclotomic_eval {n : ℕ} {q : ℝ} (hn' : 2 ≤
   have hfor : ∀ ζ' ∈ primitiveRoots n ℂ, q - 1 ≤ ‖↑q - ζ'‖ :=
     by
     intro ζ' hζ'
-    rw [mem_primitiveRoots hn] at hζ' 
+    rw [mem_primitiveRoots hn] at hζ'
     convert norm_sub_norm_le (↑q) ζ'
     · rw [Complex.norm_real, Real.norm_of_nonneg hq.le]
     · rw [hζ'.norm'_eq_one hn.ne']
@@ -246,7 +246,7 @@ theorem sub_one_pow_totient_lt_cyclotomic_eval {n : ℕ} {q : ℝ} (hn' : 2 ≤
     by
     simp only [← Units.val_lt_val, Units.val_pow_eq_pow_val, Units.val_mk0, ← NNReal.coe_lt_coe,
       hq'.le, Real.toNNReal_lt_toNNReal_iff_of_nonneg, coe_nnnorm, Complex.norm_eq_abs,
-      NNReal.coe_pow, Real.coe_toNNReal', max_eq_left, sub_nonneg] at this 
+      NNReal.coe_pow, Real.coe_toNNReal', max_eq_left, sub_nonneg] at this
     convert this
     erw [cyclotomic.eval_apply q n (algebraMap ℝ ℂ), eq_comm]
     simp only [cyclotomic_nonneg n hq'.le, Complex.coe_algebraMap, Complex.abs_ofReal, abs_eq_self]
@@ -284,7 +284,7 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
   have hfor : ∀ ζ' ∈ primitiveRoots n ℂ, ‖↑q - ζ'‖ ≤ q + 1 :=
     by
     intro ζ' hζ'
-    rw [mem_primitiveRoots hn] at hζ' 
+    rw [mem_primitiveRoots hn] at hζ'
     convert norm_sub_le (↑q) ζ'
     · rw [Complex.norm_real, Real.norm_of_nonneg (zero_le_one.trans_lt hq').le]
     · rw [hζ'.norm'_eq_one hn.ne']
@@ -301,14 +301,14 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
     refine' ⟨by exact_mod_cast hq.ne', neg_ne_zero.mpr <| hζ.ne_zero hn.ne', _⟩
     rw [Complex.arg_ofReal_of_nonneg hq.le, Ne.def, eq_comm]
     intro h
-    rw [Complex.arg_eq_zero_iff, Complex.neg_re, neg_nonneg, Complex.neg_im, neg_eq_zero] at h 
+    rw [Complex.arg_eq_zero_iff, Complex.neg_re, neg_nonneg, Complex.neg_im, neg_eq_zero] at h
     have hζ₀ : ζ ≠ 0 := by
       clear_value ζ
       rintro rfl
       exact hn.ne' (hζ.unique IsPrimitiveRoot.zero)
     have : ζ.re < 0 ∧ ζ.im = 0 := ⟨h.1.lt_of_ne _, h.2⟩
-    rw [← Complex.arg_eq_pi_iff, hζ.arg_eq_pi_iff hn.ne'] at this 
-    rw [this] at hζ 
+    rw [← Complex.arg_eq_pi_iff, hζ.arg_eq_pi_iff hn.ne'] at this
+    rw [this] at hζ
     linarith [hζ.unique <| IsPrimitiveRoot.neg_one 0 two_ne_zero.symm]
     · contrapose! hζ₀
       ext <;> simp [hζ₀, h.2]
@@ -323,7 +323,7 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
     by
     simp only [← Units.val_lt_val, Units.val_pow_eq_pow_val, Units.val_mk0, ← NNReal.coe_lt_coe,
       hq'.le, Real.toNNReal_lt_toNNReal_iff_of_nonneg, coe_nnnorm, Complex.norm_eq_abs,
-      NNReal.coe_pow, Real.coe_toNNReal', max_eq_left, sub_nonneg] at this 
+      NNReal.coe_pow, Real.coe_toNNReal', max_eq_left, sub_nonneg] at this
     convert this
     · erw [cyclotomic.eval_apply q n (algebraMap ℝ ℂ), eq_comm]
       simp [cyclotomic_nonneg n hq'.le]

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

@@ -75,7 +75,7 @@ private theorem cyclotomic_neg_one_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrdered
   simp only [Int.cast_one, Int.cast_neg]
   have h0 := cyclotomic_coeff_zero ℝ hn.le
   rw [coeff_zero_eq_eval_zero] at h0 
-  by_contra' hx
+  by_contra! hx
   have := intermediate_value_univ (-1) 0 (cyclotomic n ℝ).Continuous
   obtain ⟨y, hy : is_root _ y⟩ := this (show (0 : ℝ) ∈ Set.Icc _ _ by simpa [h0] using hx)
   rw [is_root_cyclotomic_iff] at hy 

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

@@ -3,11 +3,11 @@ Copyright (c) 2021 Eric Rodriguez. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Rodriguez
 -/
-import Mathbin.RingTheory.Polynomial.Cyclotomic.Roots
-import Mathbin.Tactic.ByContra
-import Mathbin.Topology.Algebra.Polynomial
-import Mathbin.NumberTheory.Padics.PadicVal
-import Mathbin.Analysis.Complex.Arg
+import RingTheory.Polynomial.Cyclotomic.Roots
+import Tactic.ByContra
+import Topology.Algebra.Polynomial
+import NumberTheory.Padics.PadicVal
+import Analysis.Complex.Arg
 
 #align_import ring_theory.polynomial.cyclotomic.eval from "leanprover-community/mathlib"@"2a0ce625dbb0ffbc7d1316597de0b25c1ec75303"
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Eric Rodriguez. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Rodriguez
-
-! This file was ported from Lean 3 source module ring_theory.polynomial.cyclotomic.eval
-! 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.Roots
 import Mathbin.Tactic.ByContra
@@ -14,6 +9,8 @@ import Mathbin.Topology.Algebra.Polynomial
 import Mathbin.NumberTheory.Padics.PadicVal
 import Mathbin.Analysis.Complex.Arg
 
+#align_import ring_theory.polynomial.cyclotomic.eval from "leanprover-community/mathlib"@"2a0ce625dbb0ffbc7d1316597de0b25c1ec75303"
+
 /-!
 # Evaluating cyclotomic polynomials
 

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

@@ -33,29 +33,37 @@ open Finset Nat
 
 open scoped BigOperators
 
+#print Polynomial.eval_one_cyclotomic_prime /-
 @[simp]
 theorem eval_one_cyclotomic_prime {R : Type _} [CommRing R] {p : ℕ} [hn : Fact p.Prime] :
     eval 1 (cyclotomic p R) = p := by
   simp only [cyclotomic_prime, eval_X, one_pow, Finset.sum_const, eval_pow, eval_finset_sum,
     Finset.card_range, smul_one_eq_coe]
 #align polynomial.eval_one_cyclotomic_prime Polynomial.eval_one_cyclotomic_prime
+-/
 
+#print Polynomial.eval₂_one_cyclotomic_prime /-
 @[simp]
 theorem eval₂_one_cyclotomic_prime {R S : Type _} [CommRing R] [Semiring S] (f : R →+* S) {p : ℕ}
     [Fact p.Prime] : eval₂ f 1 (cyclotomic p R) = p := by simp
 #align polynomial.eval₂_one_cyclotomic_prime Polynomial.eval₂_one_cyclotomic_prime
+-/
 
+#print Polynomial.eval_one_cyclotomic_prime_pow /-
 @[simp]
 theorem eval_one_cyclotomic_prime_pow {R : Type _} [CommRing R] {p : ℕ} (k : ℕ)
     [hn : Fact p.Prime] : eval 1 (cyclotomic (p ^ (k + 1)) R) = p := by
   simp only [cyclotomic_prime_pow_eq_geom_sum hn.out, eval_X, one_pow, Finset.sum_const, eval_pow,
     eval_finset_sum, Finset.card_range, smul_one_eq_coe]
 #align polynomial.eval_one_cyclotomic_prime_pow Polynomial.eval_one_cyclotomic_prime_pow
+-/
 
+#print Polynomial.eval₂_one_cyclotomic_prime_pow /-
 @[simp]
 theorem eval₂_one_cyclotomic_prime_pow {R S : Type _} [CommRing R] [Semiring S] (f : R →+* S)
     {p : ℕ} (k : ℕ) [Fact p.Prime] : eval₂ f 1 (cyclotomic (p ^ (k + 1)) R) = p := by simp
 #align polynomial.eval₂_one_cyclotomic_prime_pow Polynomial.eval₂_one_cyclotomic_prime_pow
+-/
 
 private theorem cyclotomic_neg_one_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrderedCommRing R] :
     0 < eval (-1 : R) (cyclotomic n R) :=
@@ -77,6 +85,7 @@ private theorem cyclotomic_neg_one_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrdered
   rw [hy.eq_order_of] at hn 
   exact hn.not_le LinearOrderedRing.orderOf_le_two
 
+#print Polynomial.cyclotomic_pos /-
 theorem cyclotomic_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrderedCommRing R] (x : R) :
     0 < eval x (cyclotomic n R) :=
   by
@@ -123,7 +132,9 @@ theorem cyclotomic_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrderedCommRing R] (x :
       exact hn'.ne' hi.2.2.1
     · simpa only [eval_X, eval_one, cyclotomic_two, eval_add] using h.right.le
 #align polynomial.cyclotomic_pos Polynomial.cyclotomic_pos
+-/
 
+#print Polynomial.cyclotomic_pos_and_nonneg /-
 theorem cyclotomic_pos_and_nonneg (n : ℕ) {R} [LinearOrderedCommRing R] (x : R) :
     (1 < x → 0 < eval x (cyclotomic n R)) ∧ (1 ≤ x → 0 ≤ eval x (cyclotomic n R)) :=
   by
@@ -135,7 +146,9 @@ theorem cyclotomic_pos_and_nonneg (n : ℕ) {R} [LinearOrderedCommRing R] (x : R
   · have : 2 < n + 3 := by decide
     constructor <;> intro <;> [skip; apply le_of_lt] <;> apply cyclotomic_pos this
 #align polynomial.cyclotomic_pos_and_nonneg Polynomial.cyclotomic_pos_and_nonneg
+-/
 
+#print Polynomial.cyclotomic_pos' /-
 /-- Cyclotomic polynomials are always positive on inputs larger than one.
 Similar to `cyclotomic_pos` but with the condition on the input rather than index of the
 cyclotomic polynomial. -/
@@ -143,13 +156,17 @@ theorem cyclotomic_pos' (n : ℕ) {R} [LinearOrderedCommRing R] {x : R} (hx : 1
     0 < eval x (cyclotomic n R) :=
   (cyclotomic_pos_and_nonneg n x).1 hx
 #align polynomial.cyclotomic_pos' Polynomial.cyclotomic_pos'
+-/
 
+#print Polynomial.cyclotomic_nonneg /-
 /-- Cyclotomic polynomials are always nonnegative on inputs one or more. -/
 theorem cyclotomic_nonneg (n : ℕ) {R} [LinearOrderedCommRing R] {x : R} (hx : 1 ≤ x) :
     0 ≤ eval x (cyclotomic n R) :=
   (cyclotomic_pos_and_nonneg n x).2 hx
 #align polynomial.cyclotomic_nonneg Polynomial.cyclotomic_nonneg
+-/
 
+#print Polynomial.eval_one_cyclotomic_not_prime_pow /-
 theorem eval_one_cyclotomic_not_prime_pow {R : Type _} [Ring R] {n : ℕ}
     (h : ∀ {p : ℕ}, p.Prime → ∀ k : ℕ, p ^ k ≠ n) : eval 1 (cyclotomic n R) = 1 :=
   by
@@ -192,7 +209,9 @@ theorem eval_one_cyclotomic_not_prime_pow {R : Type _} [Ring R] {n : ℕ}
     apply Nat.succ_injective
     exact Nat.pow_right_injective hp.two_le hxy
 #align polynomial.eval_one_cyclotomic_not_prime_pow Polynomial.eval_one_cyclotomic_not_prime_pow
+-/
 
+#print Polynomial.sub_one_pow_totient_lt_cyclotomic_eval /-
 theorem sub_one_pow_totient_lt_cyclotomic_eval {n : ℕ} {q : ℝ} (hn' : 2 ≤ n) (hq' : 1 < q) :
     (q - 1) ^ totient n < (cyclotomic n ℝ).eval q :=
   by
@@ -248,14 +267,18 @@ theorem sub_one_pow_totient_lt_cyclotomic_eval {n : ℕ} {q : ℝ} (hn' : 2 ≤
       NNReal.coe_lt_coe, ← Units.val_lt_val, Units.val_mk0 _, coe_nnnorm]
     simpa only [hq'.le, Real.coe_toNNReal', max_eq_left, sub_nonneg] using hex
 #align polynomial.sub_one_pow_totient_lt_cyclotomic_eval Polynomial.sub_one_pow_totient_lt_cyclotomic_eval
+-/
 
+#print Polynomial.sub_one_pow_totient_le_cyclotomic_eval /-
 theorem sub_one_pow_totient_le_cyclotomic_eval {q : ℝ} (hq' : 1 < q) :
     ∀ n, (q - 1) ^ totient n ≤ (cyclotomic n ℝ).eval q
   | 0 => by simp only [totient_zero, pow_zero, cyclotomic_zero, eval_one]
   | 1 => by simp only [totient_one, pow_one, cyclotomic_one, eval_sub, eval_X, eval_one]
   | n + 2 => (sub_one_pow_totient_lt_cyclotomic_eval (by decide) hq').le
 #align polynomial.sub_one_pow_totient_le_cyclotomic_eval Polynomial.sub_one_pow_totient_le_cyclotomic_eval
+-/
 
+#print Polynomial.cyclotomic_eval_lt_add_one_pow_totient /-
 theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤ n) (hq' : 1 < q) :
     (cyclotomic n ℝ).eval q < (q + 1) ^ totient n :=
   by
@@ -325,7 +348,9 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
     obtain ⟨ζ, hζ, hhζ : Complex.abs _ < _⟩ := hex
     exact ⟨ζ, hζ, by simp [hhζ]⟩
 #align polynomial.cyclotomic_eval_lt_add_one_pow_totient Polynomial.cyclotomic_eval_lt_add_one_pow_totient
+-/
 
+#print Polynomial.cyclotomic_eval_le_add_one_pow_totient /-
 theorem cyclotomic_eval_le_add_one_pow_totient {q : ℝ} (hq' : 1 < q) :
     ∀ n, (cyclotomic n ℝ).eval q ≤ (q + 1) ^ totient n
   | 0 => by simp
@@ -333,7 +358,9 @@ theorem cyclotomic_eval_le_add_one_pow_totient {q : ℝ} (hq' : 1 < q) :
   | 2 => by simp
   | n + 3 => (cyclotomic_eval_lt_add_one_pow_totient (by decide) hq').le
 #align polynomial.cyclotomic_eval_le_add_one_pow_totient Polynomial.cyclotomic_eval_le_add_one_pow_totient
+-/
 
+#print Polynomial.sub_one_pow_totient_lt_natAbs_cyclotomic_eval /-
 theorem sub_one_pow_totient_lt_natAbs_cyclotomic_eval {n : ℕ} {q : ℕ} (hn' : 1 < n) (hq : q ≠ 1) :
     (q - 1) ^ totient n < ((cyclotomic n ℤ).eval ↑q).natAbs :=
   by
@@ -345,13 +372,16 @@ theorem sub_one_pow_totient_lt_natAbs_cyclotomic_eval {n : ℕ} {q : ℕ} (hn' :
   refine' (sub_one_pow_totient_lt_cyclotomic_eval hn' (Nat.one_lt_cast.2 hq')).trans_le _
   exact (cyclotomic.eval_apply (q : ℤ) n (algebraMap ℤ ℝ)).trans_le (le_abs_self _)
 #align polynomial.sub_one_pow_totient_lt_nat_abs_cyclotomic_eval Polynomial.sub_one_pow_totient_lt_natAbs_cyclotomic_eval
+-/
 
+#print Polynomial.sub_one_lt_natAbs_cyclotomic_eval /-
 theorem sub_one_lt_natAbs_cyclotomic_eval {n : ℕ} {q : ℕ} (hn' : 1 < n) (hq : q ≠ 1) :
     q - 1 < ((cyclotomic n ℤ).eval ↑q).natAbs :=
   calc
     q - 1 ≤ (q - 1) ^ totient n := Nat.le_self_pow (Nat.totient_pos <| pos_of_gt hn').ne' _
     _ < ((cyclotomic n ℤ).eval ↑q).natAbs := sub_one_pow_totient_lt_natAbs_cyclotomic_eval hn' hq
 #align polynomial.sub_one_lt_nat_abs_cyclotomic_eval Polynomial.sub_one_lt_natAbs_cyclotomic_eval
+-/
 
 end Polynomial
 

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: Eric Rodriguez
 
 ! This file was ported from Lean 3 source module ring_theory.polynomial.cyclotomic.eval
-! 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.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Analysis.Complex.Arg
 
 /-!
 # Evaluating cyclotomic polynomials
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 This file states some results about evaluating cyclotomic polynomials in various different ways.
 ## Main definitions
 * `polynomial.eval(₂)_one_cyclotomic_prime(_pow)`: `eval 1 (cyclotomic p^k R) = p`.

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -213,7 +213,7 @@ theorem sub_one_pow_totient_lt_cyclotomic_eval {n : ℕ} {q : ℝ} (hn' : 2 ≤
     rw [Complex.sameRay_iff]
     push_neg
     refine' ⟨by exact_mod_cast hq.ne', hζ.ne_zero hn.ne', _⟩
-    rw [Complex.arg_of_real_of_nonneg hq.le, Ne.def, eq_comm, hζ.arg_eq_zero_iff hn.ne']
+    rw [Complex.arg_ofReal_of_nonneg hq.le, Ne.def, eq_comm, hζ.arg_eq_zero_iff hn.ne']
     clear_value ζ
     rintro rfl
     linarith [hζ.unique IsPrimitiveRoot.one]
@@ -276,7 +276,7 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
     rw [Complex.sameRay_iff]
     push_neg
     refine' ⟨by exact_mod_cast hq.ne', neg_ne_zero.mpr <| hζ.ne_zero hn.ne', _⟩
-    rw [Complex.arg_of_real_of_nonneg hq.le, Ne.def, eq_comm]
+    rw [Complex.arg_ofReal_of_nonneg hq.le, Ne.def, eq_comm]
     intro h
     rw [Complex.arg_eq_zero_iff, Complex.neg_re, neg_nonneg, Complex.neg_im, neg_eq_zero] at h 
     have hζ₀ : ζ ≠ 0 := by

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -348,7 +348,6 @@ theorem sub_one_lt_natAbs_cyclotomic_eval {n : ℕ} {q : ℕ} (hn' : 1 < n) (hq
   calc
     q - 1 ≤ (q - 1) ^ totient n := Nat.le_self_pow (Nat.totient_pos <| pos_of_gt hn').ne' _
     _ < ((cyclotomic n ℤ).eval ↑q).natAbs := sub_one_pow_totient_lt_natAbs_cyclotomic_eval hn' hq
-    
 #align polynomial.sub_one_lt_nat_abs_cyclotomic_eval Polynomial.sub_one_lt_natAbs_cyclotomic_eval
 
 end Polynomial

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

@@ -82,7 +82,7 @@ theorem cyclotomic_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrderedCommRing R] (x :
   have hn'' : 1 < n := one_lt_two.trans hn
   dsimp at ih 
   have := prod_cyclotomic_eq_geom_sum hn' R
-  apply_fun eval x  at this 
+  apply_fun eval x at this 
   rw [← cons_self_proper_divisors hn'.ne', Finset.erase_cons_of_ne _ hn''.ne', Finset.prod_cons,
     eval_mul, eval_geom_sum] at this 
   rcases lt_trichotomy 0 (∑ i in Finset.range n, x ^ i) with (h | h | h)
@@ -169,7 +169,7 @@ theorem eval_one_cyclotomic_not_prime_pow {R : Type _} [Ring R] {n : ℕ}
     apply Finset.dvd_prod_of_mem
     simp [hn'.ne', hn.ne']
   have := prod_cyclotomic_eq_geom_sum hn' ℤ
-  apply_fun eval 1  at this 
+  apply_fun eval 1 at this 
   rw [eval_geom_sum, one_geom_sum, eval_prod, eq_comm, ←
     Finset.prod_sdiff <| @range_pow_padicValNat_subset_divisors' p _ _, Finset.prod_image] at this 
   simp_rw [eval_one_cyclotomic_prime_pow, Finset.prod_const, Finset.card_range, mul_comm] at this 

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

@@ -62,16 +62,16 @@ private theorem cyclotomic_neg_one_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrdered
     Int.cast_pos]
   suffices 0 < eval (↑(-1 : ℤ)) (cyclotomic n ℝ)
     by
-    rw [← map_cyclotomic_int n ℝ, eval_int_cast_map, Int.coe_castRingHom] at this
+    rw [← map_cyclotomic_int n ℝ, eval_int_cast_map, Int.coe_castRingHom] at this 
     exact_mod_cast this
   simp only [Int.cast_one, Int.cast_neg]
   have h0 := cyclotomic_coeff_zero ℝ hn.le
-  rw [coeff_zero_eq_eval_zero] at h0
+  rw [coeff_zero_eq_eval_zero] at h0 
   by_contra' hx
   have := intermediate_value_univ (-1) 0 (cyclotomic n ℝ).Continuous
   obtain ⟨y, hy : is_root _ y⟩ := this (show (0 : ℝ) ∈ Set.Icc _ _ by simpa [h0] using hx)
-  rw [is_root_cyclotomic_iff] at hy
-  rw [hy.eq_order_of] at hn
+  rw [is_root_cyclotomic_iff] at hy 
+  rw [hy.eq_order_of] at hn 
   exact hn.not_le LinearOrderedRing.orderOf_le_two
 
 theorem cyclotomic_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrderedCommRing R] (x : R) :
@@ -80,18 +80,18 @@ theorem cyclotomic_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrderedCommRing R] (x :
   induction' n using Nat.strong_induction_on with n ih
   have hn' : 0 < n := pos_of_gt hn
   have hn'' : 1 < n := one_lt_two.trans hn
-  dsimp at ih
+  dsimp at ih 
   have := prod_cyclotomic_eq_geom_sum hn' R
-  apply_fun eval x  at this
+  apply_fun eval x  at this 
   rw [← cons_self_proper_divisors hn'.ne', Finset.erase_cons_of_ne _ hn''.ne', Finset.prod_cons,
-    eval_mul, eval_geom_sum] at this
+    eval_mul, eval_geom_sum] at this 
   rcases lt_trichotomy 0 (∑ i in Finset.range n, x ^ i) with (h | h | h)
   · apply pos_of_mul_pos_left
     · rwa [this]
     rw [eval_prod]
     refine' Finset.prod_nonneg fun i hi => _
-    simp only [Finset.mem_erase, mem_proper_divisors] at hi
-    rw [geom_sum_pos_iff hn'.ne'] at h
+    simp only [Finset.mem_erase, mem_proper_divisors] at hi 
+    rw [geom_sum_pos_iff hn'.ne'] at h 
     cases' h with hk hx
     · refine' (ih _ hi.2.2 (Nat.two_lt_of_ne _ hi.1 _)).le <;> rintro rfl
       · exact hn'.ne' (zero_dvd_iff.mp hi.2.1)
@@ -101,11 +101,11 @@ theorem cyclotomic_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrderedCommRing R] (x :
       refine' (ih _ hi.2.2 (Nat.two_lt_of_ne _ hi.1 hk)).le
       rintro rfl
       exact hn'.ne' <| zero_dvd_iff.mp hi.2.1
-  · rw [eq_comm, geom_sum_eq_zero_iff_neg_one hn'.ne'] at h
+  · rw [eq_comm, geom_sum_eq_zero_iff_neg_one hn'.ne'] at h 
     exact h.1.symm ▸ cyclotomic_neg_one_pos hn
   · apply pos_of_mul_neg_left
     · rwa [this]
-    rw [geom_sum_neg_iff hn'.ne'] at h
+    rw [geom_sum_neg_iff hn'.ne'] at h 
     have h2 : 2 ∈ n.proper_divisors.erase 1 :=
       by
       rw [Finset.mem_erase, mem_proper_divisors]
@@ -113,10 +113,10 @@ theorem cyclotomic_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrderedCommRing R] (x :
     rw [eval_prod, ← Finset.prod_erase_mul _ _ h2]
     apply mul_nonpos_of_nonneg_of_nonpos
     · refine' Finset.prod_nonneg fun i hi => le_of_lt _
-      simp only [Finset.mem_erase, mem_proper_divisors] at hi
+      simp only [Finset.mem_erase, mem_proper_divisors] at hi 
       refine' ih _ hi.2.2.2 (Nat.two_lt_of_ne _ hi.2.1 hi.1)
       rintro rfl
-      rw [zero_dvd_iff] at hi
+      rw [zero_dvd_iff] at hi 
       exact hn'.ne' hi.2.2.1
     · simpa only [eval_X, eval_one, cyclotomic_two, eval_add] using h.right.le
 #align polynomial.cyclotomic_pos Polynomial.cyclotomic_pos
@@ -130,7 +130,7 @@ theorem cyclotomic_pos_and_nonneg (n : ℕ) {R} [LinearOrderedCommRing R] (x : R
       and_self_iff]
   · constructor <;> intro <;> linarith
   · have : 2 < n + 3 := by decide
-    constructor <;> intro <;> [skip;apply le_of_lt] <;> apply cyclotomic_pos this
+    constructor <;> intro <;> [skip; apply le_of_lt] <;> apply cyclotomic_pos this
 #align polynomial.cyclotomic_pos_and_nonneg Polynomial.cyclotomic_pos_and_nonneg
 
 /-- Cyclotomic polynomials are always positive on inputs larger than one.
@@ -169,21 +169,21 @@ theorem eval_one_cyclotomic_not_prime_pow {R : Type _} [Ring R] {n : ℕ}
     apply Finset.dvd_prod_of_mem
     simp [hn'.ne', hn.ne']
   have := prod_cyclotomic_eq_geom_sum hn' ℤ
-  apply_fun eval 1  at this
+  apply_fun eval 1  at this 
   rw [eval_geom_sum, one_geom_sum, eval_prod, eq_comm, ←
-    Finset.prod_sdiff <| @range_pow_padicValNat_subset_divisors' p _ _, Finset.prod_image] at this
-  simp_rw [eval_one_cyclotomic_prime_pow, Finset.prod_const, Finset.card_range, mul_comm] at this
-  rw [← Finset.prod_sdiff <| show {n} ⊆ _ from _] at this
+    Finset.prod_sdiff <| @range_pow_padicValNat_subset_divisors' p _ _, Finset.prod_image] at this 
+  simp_rw [eval_one_cyclotomic_prime_pow, Finset.prod_const, Finset.card_range, mul_comm] at this 
+  rw [← Finset.prod_sdiff <| show {n} ⊆ _ from _] at this 
   any_goals infer_instance
   swap
   · simp only [singleton_subset_iff, mem_sdiff, mem_erase, Ne.def, mem_divisors, dvd_refl,
       true_and_iff, mem_image, mem_range, exists_prop, not_exists, not_and]
     exact ⟨⟨hn.ne', hn'.ne'⟩, fun t _ => h hp _⟩
-  rw [← Int.natAbs_ofNat p, Int.natAbs_dvd_natAbs] at hpe
+  rw [← Int.natAbs_ofNat p, Int.natAbs_dvd_natAbs] at hpe 
   obtain ⟨t, ht⟩ := hpe
-  rw [Finset.prod_singleton, ht, mul_left_comm, mul_comm, ← mul_assoc, mul_assoc] at this
+  rw [Finset.prod_singleton, ht, mul_left_comm, mul_comm, ← mul_assoc, mul_assoc] at this 
   have : (p ^ padicValNat p n * p : ℤ) ∣ n := ⟨_, this⟩
-  simp only [← pow_succ', ← Int.natAbs_dvd_natAbs, Int.natAbs_ofNat, Int.natAbs_pow] at this
+  simp only [← pow_succ', ← Int.natAbs_dvd_natAbs, Int.natAbs_ofNat, Int.natAbs_pow] at this 
   exact pow_succ_padicValNat_not_dvd hn'.ne' this
   · rintro x - y - hxy
     apply Nat.succ_injective
@@ -198,7 +198,7 @@ theorem sub_one_pow_totient_lt_cyclotomic_eval {n : ℕ} {q : ℝ} (hn' : 2 ≤
   have hfor : ∀ ζ' ∈ primitiveRoots n ℂ, q - 1 ≤ ‖↑q - ζ'‖ :=
     by
     intro ζ' hζ'
-    rw [mem_primitiveRoots hn] at hζ'
+    rw [mem_primitiveRoots hn] at hζ' 
     convert norm_sub_norm_le (↑q) ζ'
     · rw [Complex.norm_real, Real.norm_of_nonneg hq.le]
     · rw [hζ'.norm'_eq_one hn.ne']
@@ -227,7 +227,7 @@ theorem sub_one_pow_totient_lt_cyclotomic_eval {n : ℕ} {q : ℝ} (hn' : 2 ≤
     by
     simp only [← Units.val_lt_val, Units.val_pow_eq_pow_val, Units.val_mk0, ← NNReal.coe_lt_coe,
       hq'.le, Real.toNNReal_lt_toNNReal_iff_of_nonneg, coe_nnnorm, Complex.norm_eq_abs,
-      NNReal.coe_pow, Real.coe_toNNReal', max_eq_left, sub_nonneg] at this
+      NNReal.coe_pow, Real.coe_toNNReal', max_eq_left, sub_nonneg] at this 
     convert this
     erw [cyclotomic.eval_apply q n (algebraMap ℝ ℂ), eq_comm]
     simp only [cyclotomic_nonneg n hq'.le, Complex.coe_algebraMap, Complex.abs_ofReal, abs_eq_self]
@@ -261,7 +261,7 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
   have hfor : ∀ ζ' ∈ primitiveRoots n ℂ, ‖↑q - ζ'‖ ≤ q + 1 :=
     by
     intro ζ' hζ'
-    rw [mem_primitiveRoots hn] at hζ'
+    rw [mem_primitiveRoots hn] at hζ' 
     convert norm_sub_le (↑q) ζ'
     · rw [Complex.norm_real, Real.norm_of_nonneg (zero_le_one.trans_lt hq').le]
     · rw [hζ'.norm'_eq_one hn.ne']
@@ -278,14 +278,14 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
     refine' ⟨by exact_mod_cast hq.ne', neg_ne_zero.mpr <| hζ.ne_zero hn.ne', _⟩
     rw [Complex.arg_of_real_of_nonneg hq.le, Ne.def, eq_comm]
     intro h
-    rw [Complex.arg_eq_zero_iff, Complex.neg_re, neg_nonneg, Complex.neg_im, neg_eq_zero] at h
+    rw [Complex.arg_eq_zero_iff, Complex.neg_re, neg_nonneg, Complex.neg_im, neg_eq_zero] at h 
     have hζ₀ : ζ ≠ 0 := by
       clear_value ζ
       rintro rfl
       exact hn.ne' (hζ.unique IsPrimitiveRoot.zero)
     have : ζ.re < 0 ∧ ζ.im = 0 := ⟨h.1.lt_of_ne _, h.2⟩
-    rw [← Complex.arg_eq_pi_iff, hζ.arg_eq_pi_iff hn.ne'] at this
-    rw [this] at hζ
+    rw [← Complex.arg_eq_pi_iff, hζ.arg_eq_pi_iff hn.ne'] at this 
+    rw [this] at hζ 
     linarith [hζ.unique <| IsPrimitiveRoot.neg_one 0 two_ne_zero.symm]
     · contrapose! hζ₀
       ext <;> simp [hζ₀, h.2]
@@ -300,7 +300,7 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
     by
     simp only [← Units.val_lt_val, Units.val_pow_eq_pow_val, Units.val_mk0, ← NNReal.coe_lt_coe,
       hq'.le, Real.toNNReal_lt_toNNReal_iff_of_nonneg, coe_nnnorm, Complex.norm_eq_abs,
-      NNReal.coe_pow, Real.coe_toNNReal', max_eq_left, sub_nonneg] at this
+      NNReal.coe_pow, Real.coe_toNNReal', max_eq_left, sub_nonneg] at this 
     convert this
     · erw [cyclotomic.eval_apply q n (algebraMap ℝ ℂ), eq_comm]
       simp [cyclotomic_nonneg n hq'.le]

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

@@ -28,7 +28,7 @@ namespace Polynomial
 
 open Finset Nat
 
-open BigOperators
+open scoped BigOperators
 
 @[simp]
 theorem eval_one_cyclotomic_prime {R : Type _} [CommRing R] {p : ℕ} [hn : Fact p.Prime] :

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

@@ -234,8 +234,7 @@ theorem sub_one_pow_totient_lt_cyclotomic_eval {n : ℕ} {q : ℝ} (hn' : 2 ≤
   simp only [cyclotomic_eq_prod_X_sub_primitive_roots hζ, eval_prod, eval_C, eval_X, eval_sub,
     nnnorm_prod, Units.mk0_prod]
   convert Finset.prod_lt_prod' _ _
-  swap
-  · exact fun _ => Units.mk0 (Real.toNNReal (q - 1)) (by simp [hq'])
+  swap; · exact fun _ => Units.mk0 (Real.toNNReal (q - 1)) (by simp [hq'])
   · simp only [Complex.card_primitiveRoots, prod_const, card_attach]
   · simp only [Subtype.coe_mk, Finset.mem_attach, forall_true_left, Subtype.forall, ←
       Units.val_le_val, ← NNReal.coe_le_coe, complex.abs.nonneg, hq'.le, Units.val_mk0,
@@ -310,8 +309,7 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
   simp only [cyclotomic_eq_prod_X_sub_primitive_roots hζ, eval_prod, eval_C, eval_X, eval_sub,
     nnnorm_prod, Units.mk0_prod]
   convert Finset.prod_lt_prod' _ _
-  swap
-  · exact fun _ => Units.mk0 (Real.toNNReal (q + 1)) (by simp <;> linarith only [hq'])
+  swap; · exact fun _ => Units.mk0 (Real.toNNReal (q + 1)) (by simp <;> linarith only [hq'])
   · simp [Complex.card_primitiveRoots]
   · simp only [Subtype.coe_mk, Finset.mem_attach, forall_true_left, Subtype.forall, ←
       Units.val_le_val, ← NNReal.coe_le_coe, complex.abs.nonneg, hq'.le, Units.val_mk0,

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

@@ -73,7 +73,6 @@ private theorem cyclotomic_neg_one_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrdered
   rw [is_root_cyclotomic_iff] at hy
   rw [hy.eq_order_of] at hn
   exact hn.not_le LinearOrderedRing.orderOf_le_two
-#align polynomial.cyclotomic_neg_one_pos polynomial.cyclotomic_neg_one_pos
 
 theorem cyclotomic_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrderedCommRing R] (x : R) :
     0 < eval x (cyclotomic n R) :=

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

@@ -4,11 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Rodriguez
 
 ! This file was ported from Lean 3 source module ring_theory.polynomial.cyclotomic.eval
-! leanprover-community/mathlib commit 3f655f5297b030a87d641ad4e825af8d9679eb0b
+! leanprover-community/mathlib commit 5bfbcca0a7ffdd21cf1682e59106d6c942434a32
 ! 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.Polynomial.Cyclotomic.Roots
 import Mathbin.Tactic.ByContra
 import Mathbin.Topology.Algebra.Polynomial
 import Mathbin.NumberTheory.Padics.PadicVal

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -131,7 +131,7 @@ theorem cyclotomic_pos_and_nonneg (n : ℕ) {R} [LinearOrderedCommRing R] (x : R
       and_self_iff]
   · constructor <;> intro <;> linarith
   · have : 2 < n + 3 := by decide
-    constructor <;> intro <;> [skip, apply le_of_lt] <;> apply cyclotomic_pos this
+    constructor <;> intro <;> [skip;apply le_of_lt] <;> apply cyclotomic_pos this
 #align polynomial.cyclotomic_pos_and_nonneg Polynomial.cyclotomic_pos_and_nonneg
 
 /-- Cyclotomic polynomials are always positive on inputs larger than one.

mathlib commit https://github.com/leanprover-community/mathlib/commit/d4437c68c8d350fc9d4e95e1e174409db35e30d7

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Rodriguez
 
 ! This file was ported from Lean 3 source module ring_theory.polynomial.cyclotomic.eval
-! leanprover-community/mathlib commit b13c1a07b23d09d72cd393a8e72fdd88dab90fa5
+! leanprover-community/mathlib commit 3f655f5297b030a87d641ad4e825af8d9679eb0b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -274,7 +274,7 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
     refine' ⟨ζ, (mem_primitiveRoots hn).mpr hζ, _⟩
     suffices ¬SameRay ℝ (q : ℂ) (-ζ) by
       convert norm_add_lt_of_not_sameRay this <;>
-        simp [Real.norm_of_nonneg hq.le, hζ.norm'_eq_one hn.ne', -Complex.norm_eq_abs]
+        simp [abs_of_pos hq, hζ.norm'_eq_one hn.ne', -Complex.norm_eq_abs]
     rw [Complex.sameRay_iff]
     push_neg
     refine' ⟨by exact_mod_cast hq.ne', neg_ne_zero.mpr <| hζ.ne_zero hn.ne', _⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

@@ -318,11 +318,11 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
       Units.val_le_val, ← NNReal.coe_le_coe, complex.abs.nonneg, hq'.le, Units.val_mk0,
       Real.coe_toNNReal, coe_nnnorm, Complex.norm_eq_abs, max_le_iff]
     intro x hx
-    have : Complex.AbsTheory.Complex.abs _ ≤ _ := hfor x hx
+    have : Complex.abs _ ≤ _ := hfor x hx
     simp [this]
   · simp only [Subtype.coe_mk, Finset.mem_attach, exists_true_left, Subtype.exists, ←
       NNReal.coe_lt_coe, ← Units.val_lt_val, Units.val_mk0 _, coe_nnnorm]
-    obtain ⟨ζ, hζ, hhζ : Complex.AbsTheory.Complex.abs _ < _⟩ := hex
+    obtain ⟨ζ, hζ, hhζ : Complex.abs _ < _⟩ := hex
     exact ⟨ζ, hζ, by simp [hhζ]⟩
 #align polynomial.cyclotomic_eval_lt_add_one_pow_totient Polynomial.cyclotomic_eval_lt_add_one_pow_totient
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ddec54a71a0dd025c05445d467f1a2b7d586a3ba

@@ -203,7 +203,7 @@ theorem sub_one_pow_totient_lt_cyclotomic_eval {n : ℕ} {q : ℝ} (hn' : 2 ≤
     convert norm_sub_norm_le (↑q) ζ'
     · rw [Complex.norm_real, Real.norm_of_nonneg hq.le]
     · rw [hζ'.norm'_eq_one hn.ne']
-  let ζ := Complex.exp (2 * ↑Real.pi * Complex.i / ↑n)
+  let ζ := Complex.exp (2 * ↑Real.pi * Complex.I / ↑n)
   have hζ : IsPrimitiveRoot ζ n := Complex.isPrimitiveRoot_exp n hn.ne'
   have hex : ∃ ζ' ∈ primitiveRoots n ℂ, q - 1 < ‖↑q - ζ'‖ :=
     by
@@ -221,7 +221,7 @@ theorem sub_one_pow_totient_lt_cyclotomic_eval {n : ℕ} {q : ℝ} (hn' : 2 ≤
   have : ¬eval (↑q) (cyclotomic n ℂ) = 0 :=
     by
     erw [cyclotomic.eval_apply q n (algebraMap ℝ ℂ)]
-    simpa only [Complex.coe_algebraMap, Complex.of_real_eq_zero] using (cyclotomic_pos' n hq').ne'
+    simpa only [Complex.coe_algebraMap, Complex.ofReal_eq_zero] using (cyclotomic_pos' n hq').ne'
   suffices
     Units.mk0 (Real.toNNReal (q - 1)) (by simp [hq']) ^ totient n <
       Units.mk0 ‖(cyclotomic n ℂ).eval q‖₊ (by simp [this])
@@ -231,7 +231,7 @@ theorem sub_one_pow_totient_lt_cyclotomic_eval {n : ℕ} {q : ℝ} (hn' : 2 ≤
       NNReal.coe_pow, Real.coe_toNNReal', max_eq_left, sub_nonneg] at this
     convert this
     erw [cyclotomic.eval_apply q n (algebraMap ℝ ℂ), eq_comm]
-    simp only [cyclotomic_nonneg n hq'.le, Complex.coe_algebraMap, Complex.abs_of_real, abs_eq_self]
+    simp only [cyclotomic_nonneg n hq'.le, Complex.coe_algebraMap, Complex.abs_ofReal, abs_eq_self]
   simp only [cyclotomic_eq_prod_X_sub_primitive_roots hζ, eval_prod, eval_C, eval_X, eval_sub,
     nnnorm_prod, Units.mk0_prod]
   convert Finset.prod_lt_prod' _ _
@@ -267,7 +267,7 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
     convert norm_sub_le (↑q) ζ'
     · rw [Complex.norm_real, Real.norm_of_nonneg (zero_le_one.trans_lt hq').le]
     · rw [hζ'.norm'_eq_one hn.ne']
-  let ζ := Complex.exp (2 * ↑Real.pi * Complex.i / ↑n)
+  let ζ := Complex.exp (2 * ↑Real.pi * Complex.I / ↑n)
   have hζ : IsPrimitiveRoot ζ n := Complex.isPrimitiveRoot_exp n hn.ne'
   have hex : ∃ ζ' ∈ primitiveRoots n ℂ, ‖↑q - ζ'‖ < q + 1 :=
     by
@@ -294,7 +294,7 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
   have : ¬eval (↑q) (cyclotomic n ℂ) = 0 :=
     by
     erw [cyclotomic.eval_apply q n (algebraMap ℝ ℂ)]
-    simp only [Complex.coe_algebraMap, Complex.of_real_eq_zero]
+    simp only [Complex.coe_algebraMap, Complex.ofReal_eq_zero]
     exact (cyclotomic_pos' n hq').Ne.symm
   suffices
     Units.mk0 ‖(cyclotomic n ℂ).eval q‖₊ (by simp [this]) <
@@ -318,11 +318,11 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
       Units.val_le_val, ← NNReal.coe_le_coe, complex.abs.nonneg, hq'.le, Units.val_mk0,
       Real.coe_toNNReal, coe_nnnorm, Complex.norm_eq_abs, max_le_iff]
     intro x hx
-    have : Complex.abs _ ≤ _ := hfor x hx
+    have : Complex.AbsTheory.Complex.abs _ ≤ _ := hfor x hx
     simp [this]
   · simp only [Subtype.coe_mk, Finset.mem_attach, exists_true_left, Subtype.exists, ←
       NNReal.coe_lt_coe, ← Units.val_lt_val, Units.val_mk0 _, coe_nnnorm]
-    obtain ⟨ζ, hζ, hhζ : Complex.abs _ < _⟩ := hex
+    obtain ⟨ζ, hζ, hhζ : Complex.AbsTheory.Complex.abs _ < _⟩ := hex
     exact ⟨ζ, hζ, by simp [hhζ]⟩
 #align polynomial.cyclotomic_eval_lt_add_one_pow_totient Polynomial.cyclotomic_eval_lt_add_one_pow_totient
 

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

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

@@ -155,18 +155,18 @@ theorem eval_one_cyclotomic_not_prime_pow {R : Type*} [Ring R] {n : ℕ}
   apply_fun eval 1 at this
   rw [eval_geom_sum, one_geom_sum, eval_prod, eq_comm, ←
     Finset.prod_sdiff <| @range_pow_padicValNat_subset_divisors' p _ _, Finset.prod_image] at this
-  simp_rw [eval_one_cyclotomic_prime_pow, Finset.prod_const, Finset.card_range, mul_comm] at this
-  rw [← Finset.prod_sdiff <| show {n} ⊆ _ from _] at this
-  swap
-  · simp only [singleton_subset_iff, mem_sdiff, mem_erase, Ne, mem_divisors, dvd_refl,
-      true_and_iff, mem_image, mem_range, exists_prop, not_exists, not_and]
-    exact ⟨⟨hn.ne', hn'.ne'⟩, fun t _ => h hp _⟩
-  rw [← Int.natAbs_ofNat p, Int.natAbs_dvd_natAbs] at hpe
-  obtain ⟨t, ht⟩ := hpe
-  rw [Finset.prod_singleton, ht, mul_left_comm, mul_comm, ← mul_assoc, mul_assoc] at this
-  have : (p : ℤ) ^ padicValNat p n * p ∣ n := ⟨_, this⟩
-  simp only [← _root_.pow_succ, ← Int.natAbs_dvd_natAbs, Int.natAbs_ofNat, Int.natAbs_pow] at this
-  exact pow_succ_padicValNat_not_dvd hn'.ne' this
+  · simp_rw [eval_one_cyclotomic_prime_pow, Finset.prod_const, Finset.card_range, mul_comm] at this
+    rw [← Finset.prod_sdiff <| show {n} ⊆ _ from _] at this
+    swap
+    · simp only [singleton_subset_iff, mem_sdiff, mem_erase, Ne, mem_divisors, dvd_refl,
+        true_and_iff, mem_image, mem_range, exists_prop, not_exists, not_and]
+      exact ⟨⟨hn.ne', hn'.ne'⟩, fun t _ => h hp _⟩
+    rw [← Int.natAbs_ofNat p, Int.natAbs_dvd_natAbs] at hpe
+    obtain ⟨t, ht⟩ := hpe
+    rw [Finset.prod_singleton, ht, mul_left_comm, mul_comm, ← mul_assoc, mul_assoc] at this
+    have : (p : ℤ) ^ padicValNat p n * p ∣ n := ⟨_, this⟩
+    simp only [← _root_.pow_succ, ← Int.natAbs_dvd_natAbs, Int.natAbs_ofNat, Int.natAbs_pow] at this
+    exact pow_succ_padicValNat_not_dvd hn'.ne' this
   · rintro x - y - hxy
     apply Nat.succ_injective
     exact Nat.pow_right_injective hp.two_le hxy
@@ -260,9 +260,9 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
       rintro rfl
       exact hn.ne' (hζ.unique IsPrimitiveRoot.zero)
     have : ζ.re < 0 ∧ ζ.im = 0 := ⟨h.1.lt_of_ne ?_, h.2⟩
-    rw [← Complex.arg_eq_pi_iff, hζ.arg_eq_pi_iff hn.ne'] at this
-    rw [this] at hζ
-    linarith [hζ.unique <| IsPrimitiveRoot.neg_one 0 two_ne_zero.symm]
+    · rw [← Complex.arg_eq_pi_iff, hζ.arg_eq_pi_iff hn.ne'] at this
+      rw [this] at hζ
+      linarith [hζ.unique <| IsPrimitiveRoot.neg_one 0 two_ne_zero.symm]
     · contrapose! hζ₀
       apply Complex.ext <;> simp [hζ₀, h.2]
   have : ¬eval (↑q) (cyclotomic n ℂ) = 0 := by

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

@@ -54,10 +54,10 @@ theorem eval₂_one_cyclotomic_prime_pow {R S : Type*} [CommRing R] [Semiring S]
 private theorem cyclotomic_neg_one_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrderedCommRing R] :
     0 < eval (-1 : R) (cyclotomic n R) := by
   haveI := NeZero.of_gt hn
-  rw [← map_cyclotomic_int, ← Int.cast_one, ← Int.cast_neg, eval_int_cast_map, Int.coe_castRingHom,
+  rw [← map_cyclotomic_int, ← Int.cast_one, ← Int.cast_neg, eval_intCast_map, Int.coe_castRingHom,
     Int.cast_pos]
   suffices 0 < eval (↑(-1 : ℤ)) (cyclotomic n ℝ) by
-    rw [← map_cyclotomic_int n ℝ, eval_int_cast_map, Int.coe_castRingHom] at this
+    rw [← map_cyclotomic_int n ℝ, eval_intCast_map, Int.coe_castRingHom] at this
     simpa only [Int.cast_pos] using this
   simp only [Int.cast_one, Int.cast_neg]
   have h0 := cyclotomic_coeff_zero ℝ hn.le
@@ -144,7 +144,7 @@ theorem eval_one_cyclotomic_not_prime_pow {R : Type*} [Ring R] {n : ℕ}
   · simp
   have hn : 1 < n := one_lt_iff_ne_zero_and_ne_one.mpr ⟨hn'.ne', (h Nat.prime_two 0).symm⟩
   rsuffices h | h : eval 1 (cyclotomic n ℤ) = 1 ∨ eval 1 (cyclotomic n ℤ) = -1
-  · have := eval_int_cast_map (Int.castRingHom R) (cyclotomic n ℤ) 1
+  · have := eval_intCast_map (Int.castRingHom R) (cyclotomic n ℤ) 1
     simpa only [map_cyclotomic, Int.cast_one, h, eq_intCast] using this
   · exfalso
     linarith [cyclotomic_nonneg n (le_refl (1 : ℤ))]

@@ -158,7 +158,7 @@ theorem eval_one_cyclotomic_not_prime_pow {R : Type*} [Ring R] {n : ℕ}
   simp_rw [eval_one_cyclotomic_prime_pow, Finset.prod_const, Finset.card_range, mul_comm] at this
   rw [← Finset.prod_sdiff <| show {n} ⊆ _ from _] at this
   swap
-  · simp only [singleton_subset_iff, mem_sdiff, mem_erase, Ne.def, mem_divisors, dvd_refl,
+  · simp only [singleton_subset_iff, mem_sdiff, mem_erase, Ne, mem_divisors, dvd_refl,
       true_and_iff, mem_image, mem_range, exists_prop, not_exists, not_and]
     exact ⟨⟨hn.ne', hn'.ne'⟩, fun t _ => h hp _⟩
   rw [← Int.natAbs_ofNat p, Int.natAbs_dvd_natAbs] at hpe
@@ -192,7 +192,7 @@ theorem sub_one_pow_totient_lt_cyclotomic_eval {n : ℕ} {q : ℝ} (hn' : 2 ≤
     rw [Complex.sameRay_iff]
     push_neg
     refine' ⟨mod_cast hq.ne', hζ.ne_zero hn.ne', _⟩
-    rw [Complex.arg_ofReal_of_nonneg hq.le, Ne.def, eq_comm, hζ.arg_eq_zero_iff hn.ne']
+    rw [Complex.arg_ofReal_of_nonneg hq.le, Ne, eq_comm, hζ.arg_eq_zero_iff hn.ne']
     clear_value ζ
     rintro rfl
     linarith [hζ.unique IsPrimitiveRoot.one]
@@ -252,7 +252,7 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
     rw [Complex.sameRay_iff]
     push_neg
     refine' ⟨mod_cast hq.ne', neg_ne_zero.mpr <| hζ.ne_zero hn.ne', _⟩
-    rw [Complex.arg_ofReal_of_nonneg hq.le, Ne.def, eq_comm]
+    rw [Complex.arg_ofReal_of_nonneg hq.le, Ne, eq_comm]
     intro h
     rw [Complex.arg_eq_zero_iff, Complex.neg_re, neg_nonneg, Complex.neg_im, neg_eq_zero] at h
     have hζ₀ : ζ ≠ 0 := by

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.

@@ -165,7 +165,7 @@ theorem eval_one_cyclotomic_not_prime_pow {R : Type*} [Ring R] {n : ℕ}
   obtain ⟨t, ht⟩ := hpe
   rw [Finset.prod_singleton, ht, mul_left_comm, mul_comm, ← mul_assoc, mul_assoc] at this
   have : (p : ℤ) ^ padicValNat p n * p ∣ n := ⟨_, this⟩
-  simp only [← _root_.pow_succ', ← Int.natAbs_dvd_natAbs, Int.natAbs_ofNat, Int.natAbs_pow] at this
+  simp only [← _root_.pow_succ, ← Int.natAbs_dvd_natAbs, Int.natAbs_ofNat, Int.natAbs_pow] at this
   exact pow_succ_padicValNat_not_dvd hn'.ne' this
   · rintro x - y - hxy
     apply Nat.succ_injective

I removed some of the tactics that were not used and are hopefully uncontroversial arising from the linter at #11308.

As the commit messages should convey, the removed tactics are, essentially,

push_cast
norm_cast
congr
norm_num
dsimp
funext
intro
infer_instance

@@ -119,7 +119,7 @@ theorem cyclotomic_pos_and_nonneg (n : ℕ) {R} [LinearOrderedCommRing R] (x : R
     simp [cyclotomic_zero, cyclotomic_one, cyclotomic_two, succ_eq_add_one, eval_X, eval_one,
       eval_add, eval_sub, sub_nonneg, sub_pos, zero_lt_one, zero_le_one, imp_true_iff, imp_self,
       and_self_iff]
-  · constructor <;> intro <;> set_option tactic.skipAssignedInstances false in norm_num; linarith
+  · constructor <;> intro <;> linarith
   · have : 2 < n + 3 := by linarith
     constructor <;> intro <;> [skip; apply le_of_lt] <;> apply cyclotomic_pos this
 #align polynomial.cyclotomic_pos_and_nonneg Polynomial.cyclotomic_pos_and_nonneg

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>

@@ -119,7 +119,7 @@ theorem cyclotomic_pos_and_nonneg (n : ℕ) {R} [LinearOrderedCommRing R] (x : R
     simp [cyclotomic_zero, cyclotomic_one, cyclotomic_two, succ_eq_add_one, eval_X, eval_one,
       eval_add, eval_sub, sub_nonneg, sub_pos, zero_lt_one, zero_le_one, imp_true_iff, imp_self,
       and_self_iff]
-  · constructor <;> intro <;> norm_num <;> linarith
+  · constructor <;> intro <;> set_option tactic.skipAssignedInstances false in norm_num; linarith
   · have : 2 < n + 3 := by linarith
     constructor <;> intro <;> [skip; apply le_of_lt] <;> apply cyclotomic_pos this
 #align polynomial.cyclotomic_pos_and_nonneg Polynomial.cyclotomic_pos_and_nonneg

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to

• "simp can prove this"
• "simp can simplify this`"
• "was @[simp], now can be proved by simp"
• "was @[simp], but simp can prove it"
• "removed simp attribute as the equality can already be obtained by simp"
• "simp can already prove this"
• "simp already proves this"
• "simp can prove these"

@@ -34,7 +34,7 @@ theorem eval_one_cyclotomic_prime {R : Type*} [CommRing R] {p : ℕ} [hn : Fact
     Finset.card_range, smul_one_eq_coe]
 #align polynomial.eval_one_cyclotomic_prime Polynomial.eval_one_cyclotomic_prime
 
--- @[simp] -- Porting note: simp already proves this
+-- @[simp] -- Porting note (#10618): simp already proves this
 theorem eval₂_one_cyclotomic_prime {R S : Type*} [CommRing R] [Semiring S] (f : R →+* S) {p : ℕ}
     [Fact p.Prime] : eval₂ f 1 (cyclotomic p R) = p := by simp
 #align polynomial.eval₂_one_cyclotomic_prime Polynomial.eval₂_one_cyclotomic_prime
@@ -46,7 +46,7 @@ theorem eval_one_cyclotomic_prime_pow {R : Type*} [CommRing R] {p : ℕ} (k : 
     eval_finset_sum, Finset.card_range, smul_one_eq_coe]
 #align polynomial.eval_one_cyclotomic_prime_pow Polynomial.eval_one_cyclotomic_prime_pow
 
--- @[simp] -- Porting note: simp already proves this
+-- @[simp] -- Porting note (#10618): simp already proves this
 theorem eval₂_one_cyclotomic_prime_pow {R S : Type*} [CommRing R] [Semiring S] (f : R →+* S)
     {p : ℕ} (k : ℕ) [Fact p.Prime] : eval₂ f 1 (cyclotomic (p ^ (k + 1)) R) = p := by simp
 #align polynomial.eval₂_one_cyclotomic_prime_pow Polynomial.eval₂_one_cyclotomic_prime_pow

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

From LeanAPAP

@@ -307,8 +307,8 @@ theorem cyclotomic_eval_le_add_one_pow_totient {q : ℝ} (hq' : 1 < q) :
 theorem sub_one_pow_totient_lt_natAbs_cyclotomic_eval {n : ℕ} {q : ℕ} (hn' : 1 < n) (hq : q ≠ 1) :
     (q - 1) ^ totient n < ((cyclotomic n ℤ).eval ↑q).natAbs := by
   rcases hq.lt_or_lt.imp_left Nat.lt_one_iff.mp with (rfl | hq')
-  · rw [zero_tsub, zero_pow (Nat.totient_pos (pos_of_gt hn')), pos_iff_ne_zero, Int.natAbs_ne_zero,
-      Nat.cast_zero, ← coeff_zero_eq_eval_zero, cyclotomic_coeff_zero _ hn']
+  · rw [zero_tsub, zero_pow (Nat.totient_pos (pos_of_gt hn')).ne', pos_iff_ne_zero,
+      Int.natAbs_ne_zero, Nat.cast_zero, ← coeff_zero_eq_eval_zero, cyclotomic_coeff_zero _ hn']
     exact one_ne_zero
   rw [← @Nat.cast_lt ℝ, Nat.cast_pow, Nat.cast_sub hq'.le, Nat.cast_one, Int.cast_natAbs]
   refine' (sub_one_pow_totient_lt_cyclotomic_eval hn' (Nat.one_lt_cast.2 hq')).trans_le _

In accordance with this Zulip thread, this remove Complex.ext from the global ext attribute list and only enables it locally in certain files.

@@ -264,7 +264,7 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
     rw [this] at hζ
     linarith [hζ.unique <| IsPrimitiveRoot.neg_one 0 two_ne_zero.symm]
     · contrapose! hζ₀
-      ext <;> simp [hζ₀, h.2]
+      apply Complex.ext <;> simp [hζ₀, h.2]
   have : ¬eval (↑q) (cyclotomic n ℂ) = 0 := by
     erw [cyclotomic.eval_apply q n (algebraMap ℝ ℂ)]
     simp only [Complex.coe_algebraMap, Complex.ofReal_eq_zero]

To fit with the "please try harder" convention of ! tactics.

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

@@ -62,7 +62,7 @@ private theorem cyclotomic_neg_one_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrdered
   simp only [Int.cast_one, Int.cast_neg]
   have h0 := cyclotomic_coeff_zero ℝ hn.le
   rw [coeff_zero_eq_eval_zero] at h0
-  by_contra' hx
+  by_contra! hx
   have := intermediate_value_univ (-1) 0 (cyclotomic n ℝ).continuous
   obtain ⟨y, hy : IsRoot _ y⟩ := this (show (0 : ℝ) ∈ Set.Icc _ _ by simpa [h0] using hx)
   rw [@isRoot_cyclotomic_iff] at hy

We still have the exact_mod_cast tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast are the ones that don't work using the term elaborator by itself.

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

@@ -191,7 +191,7 @@ theorem sub_one_pow_totient_lt_cyclotomic_eval {n : ℕ} {q : ℝ} (hn' : 2 ≤
         simp only [hζ.norm'_eq_one hn.ne', Real.norm_of_nonneg hq.le, Complex.norm_real]
     rw [Complex.sameRay_iff]
     push_neg
-    refine' ⟨by exact_mod_cast hq.ne', hζ.ne_zero hn.ne', _⟩
+    refine' ⟨mod_cast hq.ne', hζ.ne_zero hn.ne', _⟩
     rw [Complex.arg_ofReal_of_nonneg hq.le, Ne.def, eq_comm, hζ.arg_eq_zero_iff hn.ne']
     clear_value ζ
     rintro rfl
@@ -251,7 +251,7 @@ theorem cyclotomic_eval_lt_add_one_pow_totient {n : ℕ} {q : ℝ} (hn' : 3 ≤
       · simp [abs_of_pos hq, hζ.norm'_eq_one hn.ne', -Complex.norm_eq_abs]
     rw [Complex.sameRay_iff]
     push_neg
-    refine' ⟨by exact_mod_cast hq.ne', neg_ne_zero.mpr <| hζ.ne_zero hn.ne', _⟩
+    refine' ⟨mod_cast hq.ne', neg_ne_zero.mpr <| hζ.ne_zero hn.ne', _⟩
     rw [Complex.arg_ofReal_of_nonneg hq.le, Ne.def, eq_comm]
     intro h
     rw [Complex.arg_eq_zero_iff, Complex.neg_re, neg_nonneg, Complex.neg_im, neg_eq_zero] at h

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

@@ -74,7 +74,6 @@ theorem cyclotomic_pos {n : ℕ} (hn : 2 < n) {R} [LinearOrderedCommRing R] (x :
   induction' n using Nat.strong_induction_on with n ih
   have hn' : 0 < n := pos_of_gt hn
   have hn'' : 1 < n := one_lt_two.trans hn
-  dsimp at ih
   have := prod_cyclotomic_eq_geom_sum hn' R
   apply_fun eval x at this
   rw [← cons_self_properDivisors hn'.ne', Finset.erase_cons_of_ne _ hn''.ne', Finset.prod_cons,

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

This has nice performance benefits.

@@ -28,26 +28,26 @@ open Finset Nat
 open scoped BigOperators
 
 @[simp]
-theorem eval_one_cyclotomic_prime {R : Type _} [CommRing R] {p : ℕ} [hn : Fact p.Prime] :
+theorem eval_one_cyclotomic_prime {R : Type*} [CommRing R] {p : ℕ} [hn : Fact p.Prime] :
     eval 1 (cyclotomic p R) = p := by
   simp only [cyclotomic_prime, eval_X, one_pow, Finset.sum_const, eval_pow, eval_finset_sum,
     Finset.card_range, smul_one_eq_coe]
 #align polynomial.eval_one_cyclotomic_prime Polynomial.eval_one_cyclotomic_prime
 
 -- @[simp] -- Porting note: simp already proves this
-theorem eval₂_one_cyclotomic_prime {R S : Type _} [CommRing R] [Semiring S] (f : R →+* S) {p : ℕ}
+theorem eval₂_one_cyclotomic_prime {R S : Type*} [CommRing R] [Semiring S] (f : R →+* S) {p : ℕ}
     [Fact p.Prime] : eval₂ f 1 (cyclotomic p R) = p := by simp
 #align polynomial.eval₂_one_cyclotomic_prime Polynomial.eval₂_one_cyclotomic_prime
 
 @[simp]
-theorem eval_one_cyclotomic_prime_pow {R : Type _} [CommRing R] {p : ℕ} (k : ℕ)
+theorem eval_one_cyclotomic_prime_pow {R : Type*} [CommRing R] {p : ℕ} (k : ℕ)
     [hn : Fact p.Prime] : eval 1 (cyclotomic (p ^ (k + 1)) R) = p := by
   simp only [cyclotomic_prime_pow_eq_geom_sum hn.out, eval_X, one_pow, Finset.sum_const, eval_pow,
     eval_finset_sum, Finset.card_range, smul_one_eq_coe]
 #align polynomial.eval_one_cyclotomic_prime_pow Polynomial.eval_one_cyclotomic_prime_pow
 
 -- @[simp] -- Porting note: simp already proves this
-theorem eval₂_one_cyclotomic_prime_pow {R S : Type _} [CommRing R] [Semiring S] (f : R →+* S)
+theorem eval₂_one_cyclotomic_prime_pow {R S : Type*} [CommRing R] [Semiring S] (f : R →+* S)
     {p : ℕ} (k : ℕ) [Fact p.Prime] : eval₂ f 1 (cyclotomic (p ^ (k + 1)) R) = p := by simp
 #align polynomial.eval₂_one_cyclotomic_prime_pow Polynomial.eval₂_one_cyclotomic_prime_pow
 
@@ -139,7 +139,7 @@ theorem cyclotomic_nonneg (n : ℕ) {R} [LinearOrderedCommRing R] {x : R} (hx :
   (cyclotomic_pos_and_nonneg n x).2 hx
 #align polynomial.cyclotomic_nonneg Polynomial.cyclotomic_nonneg
 
-theorem eval_one_cyclotomic_not_prime_pow {R : Type _} [Ring R] {n : ℕ}
+theorem eval_one_cyclotomic_not_prime_pow {R : Type*} [Ring R] {n : ℕ}
     (h : ∀ {p : ℕ}, p.Prime → ∀ k : ℕ, p ^ k ≠ n) : eval 1 (cyclotomic n R) = 1 := by
   rcases n.eq_zero_or_pos with (rfl | hn')
   · simp

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Eric Rodriguez. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Rodriguez
-
-! This file was ported from Lean 3 source module ring_theory.polynomial.cyclotomic.eval
-! leanprover-community/mathlib commit 5bfbcca0a7ffdd21cf1682e59106d6c942434a32
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.Polynomial.Cyclotomic.Roots
 import Mathlib.Tactic.ByContra
@@ -14,6 +9,8 @@ import Mathlib.Topology.Algebra.Polynomial
 import Mathlib.NumberTheory.Padics.PadicVal
 import Mathlib.Analysis.Complex.Arg
 
+#align_import ring_theory.polynomial.cyclotomic.eval from "leanprover-community/mathlib"@"5bfbcca0a7ffdd21cf1682e59106d6c942434a32"
+
 /-!
 # Evaluating cyclotomic polynomials
 This file states some results about evaluating cyclotomic polynomials in various different ways.