ring_theory.roots_of_unity.minpoly ⟷ Mathlib.RingTheory.RootsOfUnity.Minpoly

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

@@ -73,7 +73,7 @@ theorem separable_minpoly_mod {p : ℕ} [Fact p.Prime] (hdiv : ¬p ∣ n) :
       RingHom.map_dvd (map_ring_hom (Int.castRingHom (ZMod p))) (minpoly_dvd_X_pow_sub_one h)
   refine' separable.of_dvd (separable_X_pow_sub_C 1 _ one_ne_zero) hdvd
   by_contra hzero
-  exact hdiv ((ZMod.nat_cast_zmod_eq_zero_iff_dvd n p).1 hzero)
+  exact hdiv ((ZMod.natCast_zmod_eq_zero_iff_dvd n p).1 hzero)
 #align is_primitive_root.separable_minpoly_mod IsPrimitiveRoot.separable_minpoly_mod
 -/
 
@@ -173,7 +173,7 @@ theorem minpoly_eq_pow {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
     lt_of_lt_of_le (PartENat.coe_lt_coe.2 one_lt_two)
       (multiplicity.le_multiplicity_of_pow_dvd (dvd_trans habs Prod))
   have hfree : Squarefree (X ^ n - 1 : (ZMod p)[X]) :=
-    (separable_X_pow_sub_C 1 (fun h => hdiv <| (ZMod.nat_cast_zmod_eq_zero_iff_dvd n p).1 h)
+    (separable_X_pow_sub_C 1 (fun h => hdiv <| (ZMod.natCast_zmod_eq_zero_iff_dvd n p).1 h)
         one_ne_zero).Squarefree
   cases'
     (multiplicity.squarefree_iff_multiplicity_le_one (X ^ n - 1)).1 hfree

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

@@ -164,9 +164,9 @@ theorem minpoly_eq_pow {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
       exact minpoly_dvd_X_pow_sub_one (pow_of_prime h hprime.1 hdiv)
   replace prod := RingHom.map_dvd (map_ring_hom (Int.castRingHom (ZMod p))) Prod
   rw [coe_map_ring_hom, Polynomial.map_mul, Polynomial.map_sub, Polynomial.map_one,
-    Polynomial.map_pow, map_X] at prod 
+    Polynomial.map_pow, map_X] at prod
   obtain ⟨R, hR⟩ := minpoly_dvd_mod_p h hdiv
-  rw [hR, ← mul_assoc, ← Polynomial.map_mul, ← sq, Polynomial.map_pow] at prod 
+  rw [hR, ← mul_assoc, ← Polynomial.map_mul, ← sq, Polynomial.map_pow] at prod
   have habs : map (Int.castRingHom (ZMod p)) P ^ 2 ∣ map (Int.castRingHom (ZMod p)) P ^ 2 * R := by
     use R
   replace habs :=
@@ -179,9 +179,9 @@ theorem minpoly_eq_pow {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
     (multiplicity.squarefree_iff_multiplicity_le_one (X ^ n - 1)).1 hfree
       (map (Int.castRingHom (ZMod p)) P) with
     hle hunit
-  · rw [Nat.cast_one] at habs ; exact hle.not_lt habs
+  · rw [Nat.cast_one] at habs; exact hle.not_lt habs
   · replace hunit := degree_eq_zero_of_is_unit hunit
-    rw [degree_map_eq_of_leading_coeff_ne_zero (Int.castRingHom (ZMod p)) _] at hunit 
+    rw [degree_map_eq_of_leading_coeff_ne_zero (Int.castRingHom (ZMod p)) _] at hunit
     · exact (minpoly.degree_pos (IsIntegral h hpos)).ne' hunit
     simp only [Pmonic, eq_intCast, monic.leading_coeff, Int.cast_one, Ne.def, not_false_iff,
       one_ne_zero]

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

@@ -123,8 +123,7 @@ theorem minpoly_dvd_pow_mod {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n)
 theorem minpoly_dvd_mod_p {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
     map (Int.castRingHom (ZMod p)) (minpoly ℤ μ) ∣
       map (Int.castRingHom (ZMod p)) (minpoly ℤ (μ ^ p)) :=
-  (UniqueFactorizationMonoid.dvd_pow_iff_dvd_of_squarefree (squarefree_minpoly_mod h hdiv)
-        hprime.1.NeZero).1
+  (Squarefree.dvd_pow_iff_dvd (squarefree_minpoly_mod h hdiv) hprime.1.NeZero).1
     (minpoly_dvd_pow_mod h hdiv)
 #align is_primitive_root.minpoly_dvd_mod_p IsPrimitiveRoot.minpoly_dvd_mod_p
 -/

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

@@ -134,7 +134,58 @@ theorem minpoly_dvd_mod_p {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
 then the minimal polynomials of a primitive `n`-th root of unity `μ`
 and of `μ ^ p` are the same. -/
 theorem minpoly_eq_pow {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
-    minpoly ℤ μ = minpoly ℤ (μ ^ p) := by classical
+    minpoly ℤ μ = minpoly ℤ (μ ^ p) := by
+  classical
+  by_cases hn : n = 0
+  · simp_all
+  have hpos := Nat.pos_of_ne_zero hn
+  by_contra hdiff
+  set P := minpoly ℤ μ
+  set Q := minpoly ℤ (μ ^ p)
+  have Pmonic : P.monic := minpoly.monic (h.is_integral hpos)
+  have Qmonic : Q.monic := minpoly.monic ((h.pow_of_prime hprime.1 hdiv).IsIntegral hpos)
+  have Pirr : Irreducible P := minpoly.irreducible (h.is_integral hpos)
+  have Qirr : Irreducible Q := minpoly.irreducible ((h.pow_of_prime hprime.1 hdiv).IsIntegral hpos)
+  have PQprim : is_primitive (P * Q) := Pmonic.is_primitive.mul Qmonic.is_primitive
+  have prod : P * Q ∣ X ^ n - 1 :=
+    by
+    rw [is_primitive.int.dvd_iff_map_cast_dvd_map_cast (P * Q) (X ^ n - 1) PQprim
+        (monic_X_pow_sub_C (1 : ℤ) (ne_of_gt hpos)).IsPrimitive,
+      Polynomial.map_mul]
+    refine' IsCoprime.mul_dvd _ _ _
+    · have aux := is_primitive.int.irreducible_iff_irreducible_map_cast Pmonic.is_primitive
+      refine' (dvd_or_coprime _ _ (aux.1 Pirr)).resolve_left _
+      rw [map_dvd_map (Int.castRingHom ℚ) Int.cast_injective Pmonic]
+      intro hdiv
+      refine' hdiff (eq_of_monic_of_associated Pmonic Qmonic _)
+      exact associated_of_dvd_dvd hdiv (Pirr.dvd_symm Qirr hdiv)
+    · apply (map_dvd_map (Int.castRingHom ℚ) Int.cast_injective Pmonic).2
+      exact minpoly_dvd_X_pow_sub_one h
+    · apply (map_dvd_map (Int.castRingHom ℚ) Int.cast_injective Qmonic).2
+      exact minpoly_dvd_X_pow_sub_one (pow_of_prime h hprime.1 hdiv)
+  replace prod := RingHom.map_dvd (map_ring_hom (Int.castRingHom (ZMod p))) Prod
+  rw [coe_map_ring_hom, Polynomial.map_mul, Polynomial.map_sub, Polynomial.map_one,
+    Polynomial.map_pow, map_X] at prod 
+  obtain ⟨R, hR⟩ := minpoly_dvd_mod_p h hdiv
+  rw [hR, ← mul_assoc, ← Polynomial.map_mul, ← sq, Polynomial.map_pow] at prod 
+  have habs : map (Int.castRingHom (ZMod p)) P ^ 2 ∣ map (Int.castRingHom (ZMod p)) P ^ 2 * R := by
+    use R
+  replace habs :=
+    lt_of_lt_of_le (PartENat.coe_lt_coe.2 one_lt_two)
+      (multiplicity.le_multiplicity_of_pow_dvd (dvd_trans habs Prod))
+  have hfree : Squarefree (X ^ n - 1 : (ZMod p)[X]) :=
+    (separable_X_pow_sub_C 1 (fun h => hdiv <| (ZMod.nat_cast_zmod_eq_zero_iff_dvd n p).1 h)
+        one_ne_zero).Squarefree
+  cases'
+    (multiplicity.squarefree_iff_multiplicity_le_one (X ^ n - 1)).1 hfree
+      (map (Int.castRingHom (ZMod p)) P) with
+    hle hunit
+  · rw [Nat.cast_one] at habs ; exact hle.not_lt habs
+  · replace hunit := degree_eq_zero_of_is_unit hunit
+    rw [degree_map_eq_of_leading_coeff_ne_zero (Int.castRingHom (ZMod p)) _] at hunit 
+    · exact (minpoly.degree_pos (IsIntegral h hpos)).ne' hunit
+    simp only [Pmonic, eq_intCast, monic.leading_coeff, Int.cast_one, Ne.def, not_false_iff,
+      one_ne_zero]
 #align is_primitive_root.minpoly_eq_pow IsPrimitiveRoot.minpoly_eq_pow
 -/
 
@@ -191,12 +242,21 @@ theorem is_roots_of_minpoly [DecidableEq K] :
 
 #print IsPrimitiveRoot.totient_le_degree_minpoly /-
 /-- The degree of the minimal polynomial of `μ` is at least `totient n`. -/
-theorem totient_le_degree_minpoly : Nat.totient n ≤ (minpoly ℤ μ).natDegree := by classical
+theorem totient_le_degree_minpoly : Nat.totient n ≤ (minpoly ℤ μ).natDegree := by
+  classical
+  let P : ℤ[X] := minpoly ℤ μ
+  -- minimal polynomial of `μ`
+  let P_K : K[X] := map (Int.castRingHom K) P
+  -- minimal polynomial of `μ` sent to `K[X]`
+  calc
+    n.totient = (primitiveRoots n K).card := h.card_primitive_roots.symm
+    _ ≤ P_K.roots.to_finset.card := (Finset.card_le_card (is_roots_of_minpoly h))
+    _ ≤ P_K.roots.card := (Multiset.toFinset_card_le _)
+    _ ≤ P_K.nat_degree := (card_roots' _)
+    _ ≤ P.nat_degree := nat_degree_map_le _ _
 #align is_primitive_root.totient_le_degree_minpoly IsPrimitiveRoot.totient_le_degree_minpoly
 -/
 
--- minimal polynomial of `μ`
--- minimal polynomial of `μ` sent to `K[X]`
 end IsDomain
 
 end CommRing

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

@@ -134,58 +134,7 @@ theorem minpoly_dvd_mod_p {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
 then the minimal polynomials of a primitive `n`-th root of unity `μ`
 and of `μ ^ p` are the same. -/
 theorem minpoly_eq_pow {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
-    minpoly ℤ μ = minpoly ℤ (μ ^ p) := by
-  classical
-  by_cases hn : n = 0
-  · simp_all
-  have hpos := Nat.pos_of_ne_zero hn
-  by_contra hdiff
-  set P := minpoly ℤ μ
-  set Q := minpoly ℤ (μ ^ p)
-  have Pmonic : P.monic := minpoly.monic (h.is_integral hpos)
-  have Qmonic : Q.monic := minpoly.monic ((h.pow_of_prime hprime.1 hdiv).IsIntegral hpos)
-  have Pirr : Irreducible P := minpoly.irreducible (h.is_integral hpos)
-  have Qirr : Irreducible Q := minpoly.irreducible ((h.pow_of_prime hprime.1 hdiv).IsIntegral hpos)
-  have PQprim : is_primitive (P * Q) := Pmonic.is_primitive.mul Qmonic.is_primitive
-  have prod : P * Q ∣ X ^ n - 1 :=
-    by
-    rw [is_primitive.int.dvd_iff_map_cast_dvd_map_cast (P * Q) (X ^ n - 1) PQprim
-        (monic_X_pow_sub_C (1 : ℤ) (ne_of_gt hpos)).IsPrimitive,
-      Polynomial.map_mul]
-    refine' IsCoprime.mul_dvd _ _ _
-    · have aux := is_primitive.int.irreducible_iff_irreducible_map_cast Pmonic.is_primitive
-      refine' (dvd_or_coprime _ _ (aux.1 Pirr)).resolve_left _
-      rw [map_dvd_map (Int.castRingHom ℚ) Int.cast_injective Pmonic]
-      intro hdiv
-      refine' hdiff (eq_of_monic_of_associated Pmonic Qmonic _)
-      exact associated_of_dvd_dvd hdiv (Pirr.dvd_symm Qirr hdiv)
-    · apply (map_dvd_map (Int.castRingHom ℚ) Int.cast_injective Pmonic).2
-      exact minpoly_dvd_X_pow_sub_one h
-    · apply (map_dvd_map (Int.castRingHom ℚ) Int.cast_injective Qmonic).2
-      exact minpoly_dvd_X_pow_sub_one (pow_of_prime h hprime.1 hdiv)
-  replace prod := RingHom.map_dvd (map_ring_hom (Int.castRingHom (ZMod p))) Prod
-  rw [coe_map_ring_hom, Polynomial.map_mul, Polynomial.map_sub, Polynomial.map_one,
-    Polynomial.map_pow, map_X] at prod 
-  obtain ⟨R, hR⟩ := minpoly_dvd_mod_p h hdiv
-  rw [hR, ← mul_assoc, ← Polynomial.map_mul, ← sq, Polynomial.map_pow] at prod 
-  have habs : map (Int.castRingHom (ZMod p)) P ^ 2 ∣ map (Int.castRingHom (ZMod p)) P ^ 2 * R := by
-    use R
-  replace habs :=
-    lt_of_lt_of_le (PartENat.coe_lt_coe.2 one_lt_two)
-      (multiplicity.le_multiplicity_of_pow_dvd (dvd_trans habs Prod))
-  have hfree : Squarefree (X ^ n - 1 : (ZMod p)[X]) :=
-    (separable_X_pow_sub_C 1 (fun h => hdiv <| (ZMod.nat_cast_zmod_eq_zero_iff_dvd n p).1 h)
-        one_ne_zero).Squarefree
-  cases'
-    (multiplicity.squarefree_iff_multiplicity_le_one (X ^ n - 1)).1 hfree
-      (map (Int.castRingHom (ZMod p)) P) with
-    hle hunit
-  · rw [Nat.cast_one] at habs ; exact hle.not_lt habs
-  · replace hunit := degree_eq_zero_of_is_unit hunit
-    rw [degree_map_eq_of_leading_coeff_ne_zero (Int.castRingHom (ZMod p)) _] at hunit 
-    · exact (minpoly.degree_pos (IsIntegral h hpos)).ne' hunit
-    simp only [Pmonic, eq_intCast, monic.leading_coeff, Int.cast_one, Ne.def, not_false_iff,
-      one_ne_zero]
+    minpoly ℤ μ = minpoly ℤ (μ ^ p) := by classical
 #align is_primitive_root.minpoly_eq_pow IsPrimitiveRoot.minpoly_eq_pow
 -/
 
@@ -242,21 +191,12 @@ theorem is_roots_of_minpoly [DecidableEq K] :
 
 #print IsPrimitiveRoot.totient_le_degree_minpoly /-
 /-- The degree of the minimal polynomial of `μ` is at least `totient n`. -/
-theorem totient_le_degree_minpoly : Nat.totient n ≤ (minpoly ℤ μ).natDegree := by
-  classical
-  let P : ℤ[X] := minpoly ℤ μ
-  -- minimal polynomial of `μ`
-  let P_K : K[X] := map (Int.castRingHom K) P
-  -- minimal polynomial of `μ` sent to `K[X]`
-  calc
-    n.totient = (primitiveRoots n K).card := h.card_primitive_roots.symm
-    _ ≤ P_K.roots.to_finset.card := (Finset.card_le_card (is_roots_of_minpoly h))
-    _ ≤ P_K.roots.card := (Multiset.toFinset_card_le _)
-    _ ≤ P_K.nat_degree := (card_roots' _)
-    _ ≤ P.nat_degree := nat_degree_map_le _ _
+theorem totient_le_degree_minpoly : Nat.totient n ≤ (minpoly ℤ μ).natDegree := by classical
 #align is_primitive_root.totient_le_degree_minpoly IsPrimitiveRoot.totient_le_degree_minpoly
 -/
 
+-- minimal polynomial of `μ`
+-- minimal polynomial of `μ` sent to `K[X]`
 end IsDomain
 
 end CommRing

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

@@ -250,7 +250,7 @@ theorem totient_le_degree_minpoly : Nat.totient n ≤ (minpoly ℤ μ).natDegree
   -- minimal polynomial of `μ` sent to `K[X]`
   calc
     n.totient = (primitiveRoots n K).card := h.card_primitive_roots.symm
-    _ ≤ P_K.roots.to_finset.card := (Finset.card_le_of_subset (is_roots_of_minpoly h))
+    _ ≤ P_K.roots.to_finset.card := (Finset.card_le_card (is_roots_of_minpoly h))
     _ ≤ P_K.roots.card := (Multiset.toFinset_card_le _)
     _ ≤ P_K.nat_degree := (card_roots' _)
     _ ≤ P.nat_degree := nat_degree_map_le _ _

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

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

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

@@ -193,7 +193,7 @@ theorem minpoly_eq_pow {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
 /-- If `m : ℕ` is coprime with `n`,
 then the minimal polynomials of a primitive `n`-th root of unity `μ`
 and of `μ ^ m` are the same. -/
-theorem minpoly_eq_pow_coprime {m : ℕ} (hcop : Nat.coprime m n) : minpoly ℤ μ = minpoly ℤ (μ ^ m) :=
+theorem minpoly_eq_pow_coprime {m : ℕ} (hcop : Nat.Coprime m n) : minpoly ℤ μ = minpoly ℤ (μ ^ m) :=
   by
   revert n hcop
   refine' UniqueFactorizationMonoid.induction_on_prime m _ _ _
@@ -204,11 +204,11 @@ theorem minpoly_eq_pow_coprime {m : ℕ} (hcop : Nat.coprime m n) : minpoly ℤ
     congr
     simp [nat.is_unit_iff.mp hunit]
   · intro a p ha hprime hind n hcop h
-    rw [hind (Nat.coprime.coprime_mul_left hcop) h]; clear hind
+    rw [hind (Nat.Coprime.coprime_mul_left hcop) h]; clear hind
     replace hprime := hprime.nat_prime
-    have hdiv := (Nat.Prime.coprime_iff_not_dvd hprime).1 (Nat.coprime.coprime_mul_right hcop)
+    have hdiv := (Nat.Prime.coprime_iff_not_dvd hprime).1 (Nat.Coprime.coprime_mul_right hcop)
     haveI := Fact.mk hprime
-    rw [minpoly_eq_pow (h.pow_of_coprime a (Nat.coprime.coprime_mul_left hcop)) hdiv]
+    rw [minpoly_eq_pow (h.pow_of_coprime a (Nat.Coprime.coprime_mul_left hcop)) hdiv]
     congr 1
     ring
 #align is_primitive_root.minpoly_eq_pow_coprime IsPrimitiveRoot.minpoly_eq_pow_coprime
@@ -218,7 +218,7 @@ theorem minpoly_eq_pow_coprime {m : ℕ} (hcop : Nat.coprime m n) : minpoly ℤ
 /-- If `m : ℕ` is coprime with `n`,
 then the minimal polynomial of a primitive `n`-th root of unity `μ`
 has `μ ^ m` as root. -/
-theorem pow_isRoot_minpoly {m : ℕ} (hcop : Nat.coprime m n) :
+theorem pow_isRoot_minpoly {m : ℕ} (hcop : Nat.Coprime m n) :
     IsRoot (map (Int.castRingHom K) (minpoly ℤ μ)) (μ ^ m) := by
   simpa [minpoly_eq_pow_coprime h hcop, eval_map, aeval_def (μ ^ m) _] using minpoly.aeval ℤ (μ ^ m)
 #align is_primitive_root.pow_is_root_minpoly IsPrimitiveRoot.pow_isRoot_minpoly

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca, Johan Commelin
-
-! This file was ported from Lean 3 source module ring_theory.roots_of_unity.minpoly
-! 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.RootsOfUnity.Basic
 import Mathbin.FieldTheory.Minpoly.IsIntegrallyClosed
 
+#align_import ring_theory.roots_of_unity.minpoly from "leanprover-community/mathlib"@"2a0ce625dbb0ffbc7d1316597de0b25c1ec75303"
+
 /-!
 # Minimal polynomial of roots of unity
 

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

@@ -37,6 +37,7 @@ section CommRing
 
 variable {n : ℕ} {K : Type _} [CommRing K] {μ : K} (h : IsPrimitiveRoot μ n) (hpos : 0 < n)
 
+#print IsPrimitiveRoot.isIntegral /-
 /-- `μ` is integral over `ℤ`. -/
 theorem isIntegral : IsIntegral ℤ μ := by
   use X ^ n - 1
@@ -46,11 +47,13 @@ theorem isIntegral : IsIntegral ℤ μ := by
     simp only [((IsPrimitiveRoot.iff_def μ n).mp h).left, eval₂_one, eval₂_X_pow, eval₂_sub,
       sub_self]
 #align is_primitive_root.is_integral IsPrimitiveRoot.isIntegral
+-/
 
 section IsDomain
 
 variable [IsDomain K] [CharZero K]
 
+#print IsPrimitiveRoot.minpoly_dvd_x_pow_sub_one /-
 /-- The minimal polynomial of a root of unity `μ` divides `X ^ n - 1`. -/
 theorem minpoly_dvd_x_pow_sub_one : minpoly ℤ μ ∣ X ^ n - 1 :=
   by
@@ -61,7 +64,9 @@ theorem minpoly_dvd_x_pow_sub_one : minpoly ℤ μ ∣ X ^ n - 1 :=
   simp only [((IsPrimitiveRoot.iff_def μ n).mp h).left, aeval_X_pow, eq_intCast, Int.cast_one,
     aeval_one, AlgHom.map_sub, sub_self]
 #align is_primitive_root.minpoly_dvd_X_pow_sub_one IsPrimitiveRoot.minpoly_dvd_x_pow_sub_one
+-/
 
+#print IsPrimitiveRoot.separable_minpoly_mod /-
 /-- The reduction modulo `p` of the minimal polynomial of a root of unity `μ` is separable. -/
 theorem separable_minpoly_mod {p : ℕ} [Fact p.Prime] (hdiv : ¬p ∣ n) :
     Separable (map (Int.castRingHom (ZMod p)) (minpoly ℤ μ)) :=
@@ -73,13 +78,17 @@ theorem separable_minpoly_mod {p : ℕ} [Fact p.Prime] (hdiv : ¬p ∣ n) :
   by_contra hzero
   exact hdiv ((ZMod.nat_cast_zmod_eq_zero_iff_dvd n p).1 hzero)
 #align is_primitive_root.separable_minpoly_mod IsPrimitiveRoot.separable_minpoly_mod
+-/
 
+#print IsPrimitiveRoot.squarefree_minpoly_mod /-
 /-- The reduction modulo `p` of the minimal polynomial of a root of unity `μ` is squarefree. -/
 theorem squarefree_minpoly_mod {p : ℕ} [Fact p.Prime] (hdiv : ¬p ∣ n) :
     Squarefree (map (Int.castRingHom (ZMod p)) (minpoly ℤ μ)) :=
   (separable_minpoly_mod h hdiv).Squarefree
 #align is_primitive_root.squarefree_minpoly_mod IsPrimitiveRoot.squarefree_minpoly_mod
+-/
 
+#print IsPrimitiveRoot.minpoly_dvd_expand /-
 /- Let `P` be the minimal polynomial of a root of unity `μ` and `Q` be the minimal polynomial of
 `μ ^ p`, where `p` is a natural number that does not divide `n`. Then `P` divides `expand ℤ p Q`. -/
 theorem minpoly_dvd_expand {p : ℕ} (hdiv : ¬p ∣ n) : minpoly ℤ μ ∣ expand ℤ p (minpoly ℤ (μ ^ p)) :=
@@ -92,7 +101,9 @@ theorem minpoly_dvd_expand {p : ℕ} (hdiv : ¬p ∣ n) : minpoly ℤ μ ∣ exp
       eval_comp, eval_pow, eval_X, ← eval₂_eq_eval_map, ← aeval_def]
     exact minpoly.aeval _ _
 #align is_primitive_root.minpoly_dvd_expand IsPrimitiveRoot.minpoly_dvd_expand
+-/
 
+#print IsPrimitiveRoot.minpoly_dvd_pow_mod /-
 /- Let `P` be the minimal polynomial of a root of unity `μ` and `Q` be the minimal polynomial of
 `μ ^ p`, where `p` is a prime that does not divide `n`. Then `P` divides `Q ^ p` modulo `p`. -/
 theorem minpoly_dvd_pow_mod {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
@@ -107,7 +118,9 @@ theorem minpoly_dvd_pow_mod {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n)
   apply RingHom.map_dvd (map_ring_hom (Int.castRingHom (ZMod p)))
   exact minpoly_dvd_expand h hdiv
 #align is_primitive_root.minpoly_dvd_pow_mod IsPrimitiveRoot.minpoly_dvd_pow_mod
+-/
 
+#print IsPrimitiveRoot.minpoly_dvd_mod_p /-
 /- Let `P` be the minimal polynomial of a root of unity `μ` and `Q` be the minimal polynomial of
 `μ ^ p`, where `p` is a prime that does not divide `n`. Then `P` divides `Q` modulo `p`. -/
 theorem minpoly_dvd_mod_p {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
@@ -117,7 +130,9 @@ theorem minpoly_dvd_mod_p {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
         hprime.1.NeZero).1
     (minpoly_dvd_pow_mod h hdiv)
 #align is_primitive_root.minpoly_dvd_mod_p IsPrimitiveRoot.minpoly_dvd_mod_p
+-/
 
+#print IsPrimitiveRoot.minpoly_eq_pow /-
 /-- If `p` is a prime that does not divide `n`,
 then the minimal polynomials of a primitive `n`-th root of unity `μ`
 and of `μ ^ p` are the same. -/
@@ -175,7 +190,9 @@ theorem minpoly_eq_pow {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
     simp only [Pmonic, eq_intCast, monic.leading_coeff, Int.cast_one, Ne.def, not_false_iff,
       one_ne_zero]
 #align is_primitive_root.minpoly_eq_pow IsPrimitiveRoot.minpoly_eq_pow
+-/
 
+#print IsPrimitiveRoot.minpoly_eq_pow_coprime /-
 /-- If `m : ℕ` is coprime with `n`,
 then the minimal polynomials of a primitive `n`-th root of unity `μ`
 and of `μ ^ m` are the same. -/
@@ -198,7 +215,9 @@ theorem minpoly_eq_pow_coprime {m : ℕ} (hcop : Nat.coprime m n) : minpoly ℤ
     congr 1
     ring
 #align is_primitive_root.minpoly_eq_pow_coprime IsPrimitiveRoot.minpoly_eq_pow_coprime
+-/
 
+#print IsPrimitiveRoot.pow_isRoot_minpoly /-
 /-- If `m : ℕ` is coprime with `n`,
 then the minimal polynomial of a primitive `n`-th root of unity `μ`
 has `μ ^ m` as root. -/
@@ -206,7 +225,9 @@ theorem pow_isRoot_minpoly {m : ℕ} (hcop : Nat.coprime m n) :
     IsRoot (map (Int.castRingHom K) (minpoly ℤ μ)) (μ ^ m) := by
   simpa [minpoly_eq_pow_coprime h hcop, eval_map, aeval_def (μ ^ m) _] using minpoly.aeval ℤ (μ ^ m)
 #align is_primitive_root.pow_is_root_minpoly IsPrimitiveRoot.pow_isRoot_minpoly
+-/
 
+#print IsPrimitiveRoot.is_roots_of_minpoly /-
 /-- `primitive_roots n K` is a subset of the roots of the minimal polynomial of a primitive
 `n`-th root of unity `μ`. -/
 theorem is_roots_of_minpoly [DecidableEq K] :
@@ -220,7 +241,9 @@ theorem is_roots_of_minpoly [DecidableEq K] :
     mem_roots (map_monic_ne_zero <| minpoly.monic <| IsIntegral h hpos)] using
     pow_is_root_minpoly h hcop
 #align is_primitive_root.is_roots_of_minpoly IsPrimitiveRoot.is_roots_of_minpoly
+-/
 
+#print IsPrimitiveRoot.totient_le_degree_minpoly /-
 /-- The degree of the minimal polynomial of `μ` is at least `totient n`. -/
 theorem totient_le_degree_minpoly : Nat.totient n ≤ (minpoly ℤ μ).natDegree := by
   classical
@@ -235,6 +258,7 @@ theorem totient_le_degree_minpoly : Nat.totient n ≤ (minpoly ℤ μ).natDegree
     _ ≤ P_K.nat_degree := (card_roots' _)
     _ ≤ P.nat_degree := nat_degree_map_le _ _
 #align is_primitive_root.totient_le_degree_minpoly IsPrimitiveRoot.totient_le_degree_minpoly
+-/
 
 end IsDomain
 

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, Johan Commelin
 
 ! This file was ported from Lean 3 source module ring_theory.roots_of_unity.minpoly
-! leanprover-community/mathlib commit 7fdeecc0d03cd40f7a165e6cf00a4d2286db599f
+! leanprover-community/mathlib commit 2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.FieldTheory.Minpoly.IsIntegrallyClosed
 /-!
 # Minimal polynomial of roots of unity
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We gather several results about minimal polynomial of root of unity.
 
 ## Main results

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

@@ -34,8 +34,6 @@ section CommRing
 
 variable {n : ℕ} {K : Type _} [CommRing K] {μ : K} (h : IsPrimitiveRoot μ n) (hpos : 0 < n)
 
-include n μ h hpos
-
 /-- `μ` is integral over `ℤ`. -/
 theorem isIntegral : IsIntegral ℤ μ := by
   use X ^ n - 1
@@ -50,8 +48,6 @@ section IsDomain
 
 variable [IsDomain K] [CharZero K]
 
-omit hpos
-
 /-- The minimal polynomial of a root of unity `μ` divides `X ^ n - 1`. -/
 theorem minpoly_dvd_x_pow_sub_one : minpoly ℤ μ ∣ X ^ n - 1 :=
   by

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

@@ -235,7 +235,6 @@ theorem totient_le_degree_minpoly : Nat.totient n ≤ (minpoly ℤ μ).natDegree
     _ ≤ P_K.roots.card := (Multiset.toFinset_card_le _)
     _ ≤ P_K.nat_degree := (card_roots' _)
     _ ≤ P.nat_degree := nat_degree_map_le _ _
-    
 #align is_primitive_root.totient_le_degree_minpoly IsPrimitiveRoot.totient_le_degree_minpoly
 
 end IsDomain

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

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.

@@ -68,7 +68,7 @@ theorem separable_minpoly_mod {p : ℕ} [Fact p.Prime] (hdiv : ¬p ∣ n) :
     simp only [map_sub, map_pow, coe_mapRingHom, map_X, map_one]
   refine' Separable.of_dvd (separable_X_pow_sub_C 1 _ one_ne_zero) hdvd
   by_contra hzero
-  exact hdiv ((ZMod.nat_cast_zmod_eq_zero_iff_dvd n p).1 hzero)
+  exact hdiv ((ZMod.natCast_zmod_eq_zero_iff_dvd n p).1 hzero)
 #align is_primitive_root.separable_minpoly_mod IsPrimitiveRoot.separable_minpoly_mod
 
 /-- The reduction modulo `p` of the minimal polynomial of a root of unity `μ` is squarefree. -/
@@ -155,7 +155,7 @@ theorem minpoly_eq_pow {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
     lt_of_lt_of_le (PartENat.coe_lt_coe.2 one_lt_two)
       (multiplicity.le_multiplicity_of_pow_dvd (dvd_trans habs prod))
   have hfree : Squarefree (X ^ n - 1 : (ZMod p)[X]) :=
-    (separable_X_pow_sub_C 1 (fun h => hdiv <| (ZMod.nat_cast_zmod_eq_zero_iff_dvd n p).1 h)
+    (separable_X_pow_sub_C 1 (fun h => hdiv <| (ZMod.natCast_zmod_eq_zero_iff_dvd n p).1 h)
         one_ne_zero).squarefree
   cases'
     (multiplicity.squarefree_iff_multiplicity_le_one (X ^ n - 1)).1 hfree

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

@@ -225,9 +225,9 @@ theorem totient_le_degree_minpoly : Nat.totient n ≤ (minpoly ℤ μ).natDegree
   -- minimal polynomial of `μ` sent to `K[X]`
   calc
     n.totient = (primitiveRoots n K).card := h.card_primitiveRoots.symm
-    _ ≤ P_K.roots.toFinset.card := (Finset.card_le_card (is_roots_of_minpoly h))
-    _ ≤ Multiset.card P_K.roots := (Multiset.toFinset_card_le _)
-    _ ≤ P_K.natDegree := (card_roots' _)
+    _ ≤ P_K.roots.toFinset.card := Finset.card_le_card (is_roots_of_minpoly h)
+    _ ≤ Multiset.card P_K.roots := Multiset.toFinset_card_le _
+    _ ≤ P_K.natDegree := card_roots' _
     _ ≤ P.natDegree := natDegree_map_le _ _
 #align is_primitive_root.totient_le_degree_minpoly IsPrimitiveRoot.totient_le_degree_minpoly
 

All of these changes appear to be oversights to me.

@@ -77,7 +77,7 @@ theorem squarefree_minpoly_mod {p : ℕ} [Fact p.Prime] (hdiv : ¬p ∣ n) :
   (separable_minpoly_mod h hdiv).squarefree
 #align is_primitive_root.squarefree_minpoly_mod IsPrimitiveRoot.squarefree_minpoly_mod
 
-/- Let `P` be the minimal polynomial of a root of unity `μ` and `Q` be the minimal polynomial of
+/-- Let `P` be the minimal polynomial of a root of unity `μ` and `Q` be the minimal polynomial of
 `μ ^ p`, where `p` is a natural number that does not divide `n`. Then `P` divides `expand ℤ p Q`. -/
 theorem minpoly_dvd_expand {p : ℕ} (hdiv : ¬p ∣ n) :
     minpoly ℤ μ ∣ expand ℤ p (minpoly ℤ (μ ^ p)) := by
@@ -90,7 +90,7 @@ theorem minpoly_dvd_expand {p : ℕ} (hdiv : ¬p ∣ n) :
     exact minpoly.aeval _ _
 #align is_primitive_root.minpoly_dvd_expand IsPrimitiveRoot.minpoly_dvd_expand
 
-/- Let `P` be the minimal polynomial of a root of unity `μ` and `Q` be the minimal polynomial of
+/-- Let `P` be the minimal polynomial of a root of unity `μ` and `Q` be the minimal polynomial of
 `μ ^ p`, where `p` is a prime that does not divide `n`. Then `P` divides `Q ^ p` modulo `p`. -/
 theorem minpoly_dvd_pow_mod {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
     map (Int.castRingHom (ZMod p)) (minpoly ℤ μ) ∣
@@ -104,7 +104,7 @@ theorem minpoly_dvd_pow_mod {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n)
   exact minpoly_dvd_expand h hdiv
 #align is_primitive_root.minpoly_dvd_pow_mod IsPrimitiveRoot.minpoly_dvd_pow_mod
 
-/- Let `P` be the minimal polynomial of a root of unity `μ` and `Q` be the minimal polynomial of
+/-- Let `P` be the minimal polynomial of a root of unity `μ` and `Q` be the minimal polynomial of
 `μ ^ p`, where `p` is a prime that does not divide `n`. Then `P` divides `Q` modulo `p`. -/
 theorem minpoly_dvd_mod_p {p : ℕ} [Fact p.Prime] (hdiv : ¬p ∣ n) :
     map (Int.castRingHom (ZMod p)) (minpoly ℤ μ) ∣

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

@@ -198,7 +198,7 @@ then the minimal polynomial of a primitive `n`-th root of unity `μ`
 has `μ ^ m` as root. -/
 theorem pow_isRoot_minpoly {m : ℕ} (hcop : Nat.Coprime m n) :
     IsRoot (map (Int.castRingHom K) (minpoly ℤ μ)) (μ ^ m) := by
-  simp only [minpoly_eq_pow_coprime h hcop, IsRoot.definition, eval_map]
+  simp only [minpoly_eq_pow_coprime h hcop, IsRoot.def, eval_map]
   exact minpoly.aeval ℤ (μ ^ m)
 #align is_primitive_root.pow_is_root_minpoly IsPrimitiveRoot.pow_isRoot_minpoly
 

@@ -165,7 +165,7 @@ theorem minpoly_eq_pow {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
   · replace hunit := degree_eq_zero_of_isUnit hunit
     rw [degree_map_eq_of_leadingCoeff_ne_zero (Int.castRingHom (ZMod p)) _] at hunit
     · exact (minpoly.degree_pos (isIntegral h hpos)).ne' hunit
-    simp only [Pmonic, eq_intCast, Monic.leadingCoeff, Int.cast_one, Ne.def, not_false_iff,
+    simp only [Pmonic, eq_intCast, Monic.leadingCoeff, Int.cast_one, Ne, not_false_iff,
       one_ne_zero]
 #align is_primitive_root.minpoly_eq_pow IsPrimitiveRoot.minpoly_eq_pow
 

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

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

@@ -198,7 +198,7 @@ then the minimal polynomial of a primitive `n`-th root of unity `μ`
 has `μ ^ m` as root. -/
 theorem pow_isRoot_minpoly {m : ℕ} (hcop : Nat.Coprime m n) :
     IsRoot (map (Int.castRingHom K) (minpoly ℤ μ)) (μ ^ m) := by
-  simp only [minpoly_eq_pow_coprime h hcop, IsRoot.def, eval_map]
+  simp only [minpoly_eq_pow_coprime h hcop, IsRoot.definition, eval_map]
   exact minpoly.aeval ℤ (μ ^ m)
 #align is_primitive_root.pow_is_root_minpoly IsPrimitiveRoot.pow_isRoot_minpoly
 

• Introduce typeclass DecompositionMonoid, which says every element in the monoid is primal, i.e., whenever an element divides a product b * c, it can be factored into a product such that the factors divides b and c respectively. A domain is called pre-Schreier if its multiplicative monoid is a decomposition monoid, and these are more general than GCD domains.

• Show that any GCDMonoid is a DecompositionMonoid. In order for lemmas about DecompositionMonoids to automatically apply to UniqueFactorizationMonoids, we add instances from UniqueFactorizationMonoid α to Nonempty (NormalizedGCDMonoid α) to Nonempty (GCDMonoid α) to DecompositionMonoid α. (Zulip) See the bottom of message for an updated diagram of classes and instances.

• Introduce binary predicate IsRelPrime which says that the only common divisors of the two elements are units. Replace previous occurrences in mathlib by this predicate.

• Duplicate all lemmas about IsCoprime in Coprime/Basic (except three lemmas about smul) to IsRelPrime. Due to import constraints, they are spread into three files Algebra/Divisibility/Units (including key lemmas assuming DecompositionMonoid), GroupWithZero/Divisibility, and Coprime/Basic.

• Show IsCoprime always imply IsRelPrime and is equivalent to it in Bezout rings. To reduce duplication, the definition of Bezout rings and the GCDMonoid instance are moved from RingTheory/Bezout to RingTheory/PrincipalIdealDomain, and some results in PrincipalIdealDomain are generalized to Bezout rings.

• Remove the recently added file Squarefree/UniqueFactorizationMonoid and place the results appropriately within Squarefree/Basic. All results are generalized to DecompositionMonoid or weaker except the last one.

Zulip

With this PR, all the following instances (indicated by arrows) now work; this PR fills the central part.

                                                                          EuclideanDomain (bundled)
                                                                              ↙          ↖
                                                                 IsPrincipalIdealRing ← Field (bundled)
                                                                            ↓             ↓
         NormalizationMonoid ←          NormalizedGCDMonoid → GCDMonoid  IsBezout ← ValuationRing ← DiscreteValuationRing
                   ↓                             ↓                 ↘       ↙
Nonempty NormalizationMonoid ← Nonempty NormalizedGCDMonoid →  Nonempty GCDMonoid → IsIntegrallyClosed
                                                 ↑                    ↓
                    WfDvdMonoid ← UniqueFactorizationMonoid → DecompositionMonoid
                                                 ↑
                                       IsPrincipalIdealRing

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: Oliver Nash <github@olivernash.org>

@@ -106,12 +106,10 @@ theorem minpoly_dvd_pow_mod {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n)
 
 /- Let `P` be the minimal polynomial of a root of unity `μ` and `Q` be the minimal polynomial of
 `μ ^ p`, where `p` is a prime that does not divide `n`. Then `P` divides `Q` modulo `p`. -/
-theorem minpoly_dvd_mod_p {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
+theorem minpoly_dvd_mod_p {p : ℕ} [Fact p.Prime] (hdiv : ¬p ∣ n) :
     map (Int.castRingHom (ZMod p)) (minpoly ℤ μ) ∣
       map (Int.castRingHom (ZMod p)) (minpoly ℤ (μ ^ p)) :=
-  (UniqueFactorizationMonoid.dvd_pow_iff_dvd_of_squarefree (squarefree_minpoly_mod h hdiv)
-        hprime.1.ne_zero).1
-    (minpoly_dvd_pow_mod h hdiv)
+  (squarefree_minpoly_mod h hdiv).isRadical _ _ (minpoly_dvd_pow_mod h hdiv)
 #align is_primitive_root.minpoly_dvd_mod_p IsPrimitiveRoot.minpoly_dvd_mod_p
 
 /-- If `p` is a prime that does not divide `n`,

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>

@@ -5,6 +5,8 @@ Authors: Riccardo Brasca, Johan Commelin
 -/
 import Mathlib.RingTheory.RootsOfUnity.Basic
 import Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed
+import Mathlib.Algebra.GCDMonoid.IntegrallyClosed
+import Mathlib.FieldTheory.Finite.Basic
 
 #align_import ring_theory.roots_of_unity.minpoly from "leanprover-community/mathlib"@"7fdeecc0d03cd40f7a165e6cf00a4d2286db599f"
 

Change a few lemma names that have historically bothered me.

• Finset.card_le_of_subset → Finset.card_le_card
• Multiset.card_le_of_le → Multiset.card_le_card
• Multiset.card_lt_of_lt → Multiset.card_lt_card
• Set.ncard_le_of_subset → Set.ncard_le_ncard
• Finset.image_filter → Finset.filter_image
• CompleteLattice.finset_sup_compact_of_compact → CompleteLattice.isCompactElement_finset_sup

@@ -225,7 +225,7 @@ theorem totient_le_degree_minpoly : Nat.totient n ≤ (minpoly ℤ μ).natDegree
   -- minimal polynomial of `μ` sent to `K[X]`
   calc
     n.totient = (primitiveRoots n K).card := h.card_primitiveRoots.symm
-    _ ≤ P_K.roots.toFinset.card := (Finset.card_le_of_subset (is_roots_of_minpoly h))
+    _ ≤ P_K.roots.toFinset.card := (Finset.card_le_card (is_roots_of_minpoly h))
     _ ≤ Multiset.card P_K.roots := (Multiset.toFinset_card_le _)
     _ ≤ P_K.natDegree := (card_roots' _)
     _ ≤ P.natDegree := natDegree_map_le _ _

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

@@ -172,7 +172,7 @@ theorem minpoly_eq_pow {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
 /-- If `m : ℕ` is coprime with `n`,
 then the minimal polynomials of a primitive `n`-th root of unity `μ`
 and of `μ ^ m` are the same. -/
-theorem minpoly_eq_pow_coprime {m : ℕ} (hcop : Nat.coprime m n) :
+theorem minpoly_eq_pow_coprime {m : ℕ} (hcop : Nat.Coprime m n) :
     minpoly ℤ μ = minpoly ℤ (μ ^ m) := by
   revert n hcop
   refine' UniqueFactorizationMonoid.induction_on_prime m _ _ _
@@ -184,11 +184,11 @@ theorem minpoly_eq_pow_coprime {m : ℕ} (hcop : Nat.coprime m n) :
     simp [Nat.isUnit_iff.mp hunit]
   · intro a p _ hprime
     intro hind h hcop
-    rw [hind h (Nat.coprime.coprime_mul_left hcop)]; clear hind
+    rw [hind h (Nat.Coprime.coprime_mul_left hcop)]; clear hind
     replace hprime := hprime.nat_prime
-    have hdiv := (Nat.Prime.coprime_iff_not_dvd hprime).1 (Nat.coprime.coprime_mul_right hcop)
+    have hdiv := (Nat.Prime.coprime_iff_not_dvd hprime).1 (Nat.Coprime.coprime_mul_right hcop)
     haveI := Fact.mk hprime
-    rw [minpoly_eq_pow (h.pow_of_coprime a (Nat.coprime.coprime_mul_left hcop)) hdiv]
+    rw [minpoly_eq_pow (h.pow_of_coprime a (Nat.Coprime.coprime_mul_left hcop)) hdiv]
     congr 1
     ring
 #align is_primitive_root.minpoly_eq_pow_coprime IsPrimitiveRoot.minpoly_eq_pow_coprime
@@ -196,7 +196,7 @@ theorem minpoly_eq_pow_coprime {m : ℕ} (hcop : Nat.coprime m n) :
 /-- If `m : ℕ` is coprime with `n`,
 then the minimal polynomial of a primitive `n`-th root of unity `μ`
 has `μ ^ m` as root. -/
-theorem pow_isRoot_minpoly {m : ℕ} (hcop : Nat.coprime m n) :
+theorem pow_isRoot_minpoly {m : ℕ} (hcop : Nat.Coprime m n) :
     IsRoot (map (Int.castRingHom K) (minpoly ℤ μ)) (μ ^ m) := by
   simp only [minpoly_eq_pow_coprime h hcop, IsRoot.def, eval_map]
   exact minpoly.aeval ℤ (μ ^ m)

This reverts commit 6f8e8104. Unfortunately this bump was not linted correctly, as CI did not run runLinter Mathlib.

We can unrevert once that's fixed.

@@ -172,7 +172,7 @@ theorem minpoly_eq_pow {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
 /-- If `m : ℕ` is coprime with `n`,
 then the minimal polynomials of a primitive `n`-th root of unity `μ`
 and of `μ ^ m` are the same. -/
-theorem minpoly_eq_pow_coprime {m : ℕ} (hcop : Nat.Coprime m n) :
+theorem minpoly_eq_pow_coprime {m : ℕ} (hcop : Nat.coprime m n) :
     minpoly ℤ μ = minpoly ℤ (μ ^ m) := by
   revert n hcop
   refine' UniqueFactorizationMonoid.induction_on_prime m _ _ _
@@ -184,11 +184,11 @@ theorem minpoly_eq_pow_coprime {m : ℕ} (hcop : Nat.Coprime m n) :
     simp [Nat.isUnit_iff.mp hunit]
   · intro a p _ hprime
     intro hind h hcop
-    rw [hind h (Nat.Coprime.coprime_mul_left hcop)]; clear hind
+    rw [hind h (Nat.coprime.coprime_mul_left hcop)]; clear hind
     replace hprime := hprime.nat_prime
-    have hdiv := (Nat.Prime.coprime_iff_not_dvd hprime).1 (Nat.Coprime.coprime_mul_right hcop)
+    have hdiv := (Nat.Prime.coprime_iff_not_dvd hprime).1 (Nat.coprime.coprime_mul_right hcop)
     haveI := Fact.mk hprime
-    rw [minpoly_eq_pow (h.pow_of_coprime a (Nat.Coprime.coprime_mul_left hcop)) hdiv]
+    rw [minpoly_eq_pow (h.pow_of_coprime a (Nat.coprime.coprime_mul_left hcop)) hdiv]
     congr 1
     ring
 #align is_primitive_root.minpoly_eq_pow_coprime IsPrimitiveRoot.minpoly_eq_pow_coprime
@@ -196,7 +196,7 @@ theorem minpoly_eq_pow_coprime {m : ℕ} (hcop : Nat.Coprime m n) :
 /-- If `m : ℕ` is coprime with `n`,
 then the minimal polynomial of a primitive `n`-th root of unity `μ`
 has `μ ^ m` as root. -/
-theorem pow_isRoot_minpoly {m : ℕ} (hcop : Nat.Coprime m n) :
+theorem pow_isRoot_minpoly {m : ℕ} (hcop : Nat.coprime m n) :
     IsRoot (map (Int.castRingHom K) (minpoly ℤ μ)) (μ ^ m) := by
   simp only [minpoly_eq_pow_coprime h hcop, IsRoot.def, eval_map]
   exact minpoly.aeval ℤ (μ ^ m)

Some changes have already been review and delegated in #6910 and #7148.

The diff that needs looking at is https://github.com/leanprover-community/mathlib4/pull/7174/commits/64d6d07ee18163627c8f517eb31455411921c5ac

The std bump PR was insta-merged already!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -172,7 +172,7 @@ theorem minpoly_eq_pow {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
 /-- If `m : ℕ` is coprime with `n`,
 then the minimal polynomials of a primitive `n`-th root of unity `μ`
 and of `μ ^ m` are the same. -/
-theorem minpoly_eq_pow_coprime {m : ℕ} (hcop : Nat.coprime m n) :
+theorem minpoly_eq_pow_coprime {m : ℕ} (hcop : Nat.Coprime m n) :
     minpoly ℤ μ = minpoly ℤ (μ ^ m) := by
   revert n hcop
   refine' UniqueFactorizationMonoid.induction_on_prime m _ _ _
@@ -184,11 +184,11 @@ theorem minpoly_eq_pow_coprime {m : ℕ} (hcop : Nat.coprime m n) :
     simp [Nat.isUnit_iff.mp hunit]
   · intro a p _ hprime
     intro hind h hcop
-    rw [hind h (Nat.coprime.coprime_mul_left hcop)]; clear hind
+    rw [hind h (Nat.Coprime.coprime_mul_left hcop)]; clear hind
     replace hprime := hprime.nat_prime
-    have hdiv := (Nat.Prime.coprime_iff_not_dvd hprime).1 (Nat.coprime.coprime_mul_right hcop)
+    have hdiv := (Nat.Prime.coprime_iff_not_dvd hprime).1 (Nat.Coprime.coprime_mul_right hcop)
     haveI := Fact.mk hprime
-    rw [minpoly_eq_pow (h.pow_of_coprime a (Nat.coprime.coprime_mul_left hcop)) hdiv]
+    rw [minpoly_eq_pow (h.pow_of_coprime a (Nat.Coprime.coprime_mul_left hcop)) hdiv]
     congr 1
     ring
 #align is_primitive_root.minpoly_eq_pow_coprime IsPrimitiveRoot.minpoly_eq_pow_coprime
@@ -196,7 +196,7 @@ theorem minpoly_eq_pow_coprime {m : ℕ} (hcop : Nat.coprime m n) :
 /-- If `m : ℕ` is coprime with `n`,
 then the minimal polynomial of a primitive `n`-th root of unity `μ`
 has `μ ^ m` as root. -/
-theorem pow_isRoot_minpoly {m : ℕ} (hcop : Nat.coprime m n) :
+theorem pow_isRoot_minpoly {m : ℕ} (hcop : Nat.Coprime m n) :
     IsRoot (map (Int.castRingHom K) (minpoly ℤ μ)) (μ ^ m) := by
   simp only [minpoly_eq_pow_coprime h hcop, IsRoot.def, eval_map]
   exact minpoly.aeval ℤ (μ ^ m)

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

@@ -61,7 +61,6 @@ set_option linter.uppercaseLean3 false in
 theorem separable_minpoly_mod {p : ℕ} [Fact p.Prime] (hdiv : ¬p ∣ n) :
     Separable (map (Int.castRingHom (ZMod p)) (minpoly ℤ μ)) := by
   have hdvd : map (Int.castRingHom (ZMod p)) (minpoly ℤ μ) ∣ X ^ n - 1 := by
-    simp [Polynomial.map_pow, map_X, Polynomial.map_one, Polynomial.map_sub]
     convert RingHom.map_dvd (mapRingHom (Int.castRingHom (ZMod p)))
         (minpoly_dvd_x_pow_sub_one h)
     simp only [map_sub, map_pow, coe_mapRingHom, map_X, map_one]

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

This has nice performance benefits.

@@ -29,7 +29,7 @@ namespace IsPrimitiveRoot
 
 section CommRing
 
-variable {n : ℕ} {K : Type _} [CommRing K] {μ : K} (h : IsPrimitiveRoot μ n)
+variable {n : ℕ} {K : Type*} [CommRing K] {μ : K} (h : IsPrimitiveRoot μ n)
 
 /-- `μ` is integral over `ℤ`. -/
 -- Porting note: `hpos` was in the `variable` line, with an `omit` in mathlib3 just after this

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca, Johan Commelin
-
-! This file was ported from Lean 3 source module ring_theory.roots_of_unity.minpoly
-! leanprover-community/mathlib commit 7fdeecc0d03cd40f7a165e6cf00a4d2286db599f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.RootsOfUnity.Basic
 import Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed
 
+#align_import ring_theory.roots_of_unity.minpoly from "leanprover-community/mathlib"@"7fdeecc0d03cd40f7a165e6cf00a4d2286db599f"
+
 /-!
 # Minimal polynomial of roots of unity
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

@@ -65,7 +65,7 @@ theorem separable_minpoly_mod {p : ℕ} [Fact p.Prime] (hdiv : ¬p ∣ n) :
     Separable (map (Int.castRingHom (ZMod p)) (minpoly ℤ μ)) := by
   have hdvd : map (Int.castRingHom (ZMod p)) (minpoly ℤ μ) ∣ X ^ n - 1 := by
     simp [Polynomial.map_pow, map_X, Polynomial.map_one, Polynomial.map_sub]
-    convert  RingHom.map_dvd (mapRingHom (Int.castRingHom (ZMod p)))
+    convert RingHom.map_dvd (mapRingHom (Int.castRingHom (ZMod p)))
         (minpoly_dvd_x_pow_sub_one h)
     simp only [map_sub, map_pow, coe_mapRingHom, map_X, map_one]
   refine' Separable.of_dvd (separable_X_pow_sub_C 1 _ one_ne_zero) hdvd

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -165,7 +165,7 @@ theorem minpoly_eq_pow {p : ℕ} [hprime : Fact p.Prime] (hdiv : ¬p ∣ n) :
     (multiplicity.squarefree_iff_multiplicity_le_one (X ^ n - 1)).1 hfree
       (map (Int.castRingHom (ZMod p)) P) with
     hle hunit
-  · rw [Nat.cast_one] at habs ; exact hle.not_lt habs
+  · rw [Nat.cast_one] at habs; exact hle.not_lt habs
   · replace hunit := degree_eq_zero_of_isUnit hunit
     rw [degree_map_eq_of_leadingCoeff_ne_zero (Int.castRingHom (ZMod p)) _] at hunit
     · exact (minpoly.degree_pos (isIntegral h hpos)).ne' hunit

@@ -18,7 +18,7 @@ We gather several results about minimal polynomial of root of unity.
 
 ## Main results
 
-* `IsPrimitiveRoot.totient_le_degree_minpoly`: The degree of the minimal polynomial of a `n`-th
+* `IsPrimitiveRoot.totient_le_degree_minpoly`: The degree of the minimal polynomial of an `n`-th
   primitive root of unity is at least `totient n`.
 
 -/

• depends on: #5076

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com>