field_theory.finite.polynomial ⟷ Mathlib.FieldTheory.Finite.Polynomial

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

@@ -28,7 +28,7 @@ variable {σ : Type _}
 if and only if it is zero over `zmod n`. -/
 theorem C_dvd_iff_zmod (n : ℕ) (φ : MvPolynomial σ ℤ) :
     C (n : ℤ) ∣ φ ↔ map (Int.castRingHom (ZMod n)) φ = 0 :=
-  C_dvd_iff_map_hom_eq_zero _ _ (CharP.int_cast_eq_zero_iff (ZMod n) n) _
+  C_dvd_iff_map_hom_eq_zero _ _ (CharP.intCast_eq_zero_iff (ZMod n) n) _
 #align mv_polynomial.C_dvd_iff_zmod MvPolynomial.C_dvd_iff_zmod
 -/
 

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

@@ -6,7 +6,7 @@ Authors: Johan Commelin
 import LinearAlgebra.FiniteDimensional
 import Algebra.Module.Submodule.Ker
 import RingTheory.MvPolynomial.Basic
-import Data.MvPolynomial.Expand
+import Algebra.MvPolynomial.Expand
 import FieldTheory.Finite.Basic
 
 #align_import field_theory.finite.polynomial from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
 import LinearAlgebra.FiniteDimensional
-import LinearAlgebra.Basic
+import Algebra.Module.Submodule.Ker
 import RingTheory.MvPolynomial.Basic
 import Data.MvPolynomial.Expand
 import FieldTheory.Finite.Basic

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

@@ -132,7 +132,7 @@ variable [Field K]
 theorem eval_indicator_apply_eq_zero (a b : σ → K) (h : a ≠ b) : eval a (indicator b) = 0 :=
   by
   obtain ⟨i, hi⟩ : ∃ i, a i ≠ b i := by
-    rwa [(· ≠ ·), Function.funext_iff, Classical.not_forall] at h 
+    rwa [(· ≠ ·), Function.funext_iff, Classical.not_forall] at h
   simp only [indicator, map_prod, map_sub, map_one, map_pow, eval_X, eval_C, sub_self,
     Finset.prod_eq_zero_iff]
   refine' ⟨i, Finset.mem_univ _, _⟩
@@ -285,7 +285,7 @@ theorem eq_zero_of_eval_eq_zero [Finite σ] (p : MvPolynomial σ K) (h : ∀ v :
     (hp : p ∈ restrictDegree σ K (Fintype.card K - 1)) : p = 0 :=
   let p' : R σ K := ⟨p, hp⟩
   have : p' ∈ (evalᵢ σ K).ker := funext h
-  show p'.1 = (0 : R σ K).1 from congr_arg _ <| by rwa [ker_evalₗ, mem_bot] at this 
+  show p'.1 = (0 : R σ K).1 from congr_arg _ <| by rwa [ker_evalₗ, mem_bot] at this
 #align mv_polynomial.eq_zero_of_eval_eq_zero MvPolynomial.eq_zero_of_eval_eq_zero
 -/
 

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

@@ -100,7 +100,7 @@ theorem degrees_indicator (c : σ → K) :
   refine' le_trans (degrees_prod _ _) (Finset.sum_le_sum fun s hs => _)
   refine' le_trans (degrees_sub _ _) _
   rw [degrees_one, ← bot_eq_zero, bot_sup_eq]
-  refine' le_trans (degrees_pow _ _) (nsmul_le_nsmul_of_le_right _ _)
+  refine' le_trans (degrees_pow _ _) (nsmul_le_nsmul_right _ _)
   refine' le_trans (degrees_sub _ _) _
   rw [degrees_C, ← bot_eq_zero, sup_bot_eq]
   exact degrees_X' _

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

@@ -131,7 +131,8 @@ variable [Field K]
 #print MvPolynomial.eval_indicator_apply_eq_zero /-
 theorem eval_indicator_apply_eq_zero (a b : σ → K) (h : a ≠ b) : eval a (indicator b) = 0 :=
   by
-  obtain ⟨i, hi⟩ : ∃ i, a i ≠ b i := by rwa [(· ≠ ·), Function.funext_iff, not_forall] at h 
+  obtain ⟨i, hi⟩ : ∃ i, a i ≠ b i := by
+    rwa [(· ≠ ·), Function.funext_iff, Classical.not_forall] at h 
   simp only [indicator, map_prod, map_sub, map_one, map_pow, eval_X, eval_C, sub_self,
     Finset.prod_eq_zero_iff]
   refine' ⟨i, Finset.mem_univ _, _⟩

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

@@ -169,7 +169,7 @@ theorem map_restrict_dom_evalₗ : (restrictDegree σ K (Fintype.card K - 1)).ma
   refine' ⟨∑ n : σ → K, e n • indicator n, _, _⟩
   · exact sum_mem fun c _ => smul_mem _ _ (indicator_mem_restrict_degree _)
   · ext n
-    simp only [LinearMap.map_sum, @Finset.sum_apply (σ → K) (fun _ => K) _ _ _ _ _, Pi.smul_apply,
+    simp only [map_sum, @Finset.sum_apply (σ → K) (fun _ => K) _ _ _ _ _, Pi.smul_apply,
       LinearMap.map_smul]
     simp only [evalₗ_apply]
     trans

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

@@ -3,11 +3,11 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import Mathbin.LinearAlgebra.FiniteDimensional
-import Mathbin.LinearAlgebra.Basic
-import Mathbin.RingTheory.MvPolynomial.Basic
-import Mathbin.Data.MvPolynomial.Expand
-import Mathbin.FieldTheory.Finite.Basic
+import LinearAlgebra.FiniteDimensional
+import LinearAlgebra.Basic
+import RingTheory.MvPolynomial.Basic
+import Data.MvPolynomial.Expand
+import FieldTheory.Finite.Basic
 
 #align_import field_theory.finite.polynomial from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module field_theory.finite.polynomial
-! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.FiniteDimensional
 import Mathbin.LinearAlgebra.Basic
@@ -14,6 +9,8 @@ import Mathbin.RingTheory.MvPolynomial.Basic
 import Mathbin.Data.MvPolynomial.Expand
 import Mathbin.FieldTheory.Finite.Basic
 
+#align_import field_theory.finite.polynomial from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
+
 /-!
 ## Polynomials over finite fields
 

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

@@ -26,17 +26,20 @@ namespace MvPolynomial
 
 variable {σ : Type _}
 
+#print MvPolynomial.C_dvd_iff_zmod /-
 /-- A polynomial over the integers is divisible by `n : ℕ`
 if and only if it is zero over `zmod n`. -/
 theorem C_dvd_iff_zmod (n : ℕ) (φ : MvPolynomial σ ℤ) :
     C (n : ℤ) ∣ φ ↔ map (Int.castRingHom (ZMod n)) φ = 0 :=
   C_dvd_iff_map_hom_eq_zero _ _ (CharP.int_cast_eq_zero_iff (ZMod n) n) _
 #align mv_polynomial.C_dvd_iff_zmod MvPolynomial.C_dvd_iff_zmod
+-/
 
 section frobenius
 
 variable {p : ℕ} [Fact p.Prime]
 
+#print MvPolynomial.frobenius_zmod /-
 theorem frobenius_zmod (f : MvPolynomial σ (ZMod p)) : frobenius _ p f = expand p f :=
   by
   apply induction_on f
@@ -45,10 +48,13 @@ theorem frobenius_zmod (f : MvPolynomial σ (ZMod p)) : frobenius _ p f = expand
   · simp only [expand_X, RingHom.map_mul, AlgHom.map_mul]
     intro _ _ hf; rw [hf, frobenius_def]
 #align mv_polynomial.frobenius_zmod MvPolynomial.frobenius_zmod
+-/
 
+#print MvPolynomial.expand_zmod /-
 theorem expand_zmod (f : MvPolynomial σ (ZMod p)) : expand p f = f ^ p :=
   (frobenius_zmod _).symm
 #align mv_polynomial.expand_zmod MvPolynomial.expand_zmod
+-/
 
 end frobenius
 
@@ -79,6 +85,7 @@ section CommRing
 
 variable [CommRing K]
 
+#print MvPolynomial.eval_indicator_apply_eq_one /-
 theorem eval_indicator_apply_eq_one (a : σ → K) : eval a (indicator a) = 1 :=
   by
   nontriviality
@@ -86,7 +93,9 @@ theorem eval_indicator_apply_eq_one (a : σ → K) : eval a (indicator a) = 1 :=
   simp only [indicator, map_prod, map_sub, map_one, map_pow, eval_X, eval_C, sub_self,
     zero_pow this, sub_zero, Finset.prod_const_one]
 #align mv_polynomial.eval_indicator_apply_eq_one MvPolynomial.eval_indicator_apply_eq_one
+-/
 
+#print MvPolynomial.degrees_indicator /-
 theorem degrees_indicator (c : σ → K) :
     degrees (indicator c) ≤ ∑ s : σ, (Fintype.card K - 1) • {s} :=
   by
@@ -99,6 +108,7 @@ theorem degrees_indicator (c : σ → K) :
   rw [degrees_C, ← bot_eq_zero, sup_bot_eq]
   exact degrees_X' _
 #align mv_polynomial.degrees_indicator MvPolynomial.degrees_indicator
+-/
 
 #print MvPolynomial.indicator_mem_restrictDegree /-
 theorem indicator_mem_restrictDegree (c : σ → K) :
@@ -121,6 +131,7 @@ end CommRing
 
 variable [Field K]
 
+#print MvPolynomial.eval_indicator_apply_eq_zero /-
 theorem eval_indicator_apply_eq_zero (a b : σ → K) (h : a ≠ b) : eval a (indicator b) = 0 :=
   by
   obtain ⟨i, hi⟩ : ∃ i, a i ≠ b i := by rwa [(· ≠ ·), Function.funext_iff, not_forall] at h 
@@ -130,6 +141,7 @@ theorem eval_indicator_apply_eq_zero (a b : σ → K) (h : a ≠ b) : eval a (in
   rw [FiniteField.pow_card_sub_one_eq_one, sub_self]
   rwa [(· ≠ ·), sub_eq_zero]
 #align mv_polynomial.eval_indicator_apply_eq_zero MvPolynomial.eval_indicator_apply_eq_zero
+-/
 
 end Indicator
 
@@ -152,6 +164,7 @@ end
 
 variable [Field K] [Fintype K] [Finite σ]
 
+#print MvPolynomial.map_restrict_dom_evalₗ /-
 theorem map_restrict_dom_evalₗ : (restrictDegree σ K (Fintype.card K - 1)).map (evalₗ K σ) = ⊤ :=
   by
   cases nonempty_fintype σ
@@ -168,6 +181,7 @@ theorem map_restrict_dom_evalₗ : (restrictDegree σ K (Fintype.card K - 1)).ma
     · exact fun h => (h <| Finset.mem_univ n).elim
     · rw [eval_indicator_apply_eq_one, smul_eq_mul, mul_one]
 #align mv_polynomial.map_restrict_dom_evalₗ MvPolynomial.map_restrict_dom_evalₗ
+-/
 
 end MvPolynomial
 
@@ -215,6 +229,7 @@ end CommRing
 
 variable [Field K]
 
+#print MvPolynomial.rank_R /-
 theorem rank_R [Fintype σ] : Module.rank K (R σ K) = Fintype.card (σ → K) :=
   calc
     Module.rank K (R σ K) =
@@ -234,6 +249,7 @@ theorem rank_R [Fintype σ] : Module.rank K (R σ K) = Fintype.card (σ → K) :
     _ = (#σ → K) := (Equiv.arrowCongr (Equiv.refl σ) (Fintype.equivFin K).symm).cardinal_eq
     _ = Fintype.card (σ → K) := Cardinal.mk_fintype _
 #align mv_polynomial.rank_R MvPolynomial.rank_R
+-/
 
 instance [Finite σ] : FiniteDimensional K (R σ K) :=
   by
@@ -249,25 +265,31 @@ theorem finrank_R [Fintype σ] : FiniteDimensional.finrank K (R σ K) = Fintype.
 #align mv_polynomial.finrank_R MvPolynomial.finrank_R
 -/
 
+#print MvPolynomial.range_evalᵢ /-
 theorem range_evalᵢ [Finite σ] : (evalᵢ σ K).range = ⊤ :=
   by
   rw [evalᵢ, LinearMap.range_comp, range_subtype]
   exact map_restrict_dom_evalₗ
 #align mv_polynomial.range_evalᵢ MvPolynomial.range_evalᵢ
+-/
 
+#print MvPolynomial.ker_evalₗ /-
 theorem ker_evalₗ [Finite σ] : (evalᵢ σ K).ker = ⊥ :=
   by
   cases nonempty_fintype σ
   refine' (ker_eq_bot_iff_range_eq_top_of_finrank_eq_finrank _).mpr (range_evalᵢ _ _)
   rw [FiniteDimensional.finrank_fintype_fun_eq_card, finrank_R]
 #align mv_polynomial.ker_evalₗ MvPolynomial.ker_evalₗ
+-/
 
+#print MvPolynomial.eq_zero_of_eval_eq_zero /-
 theorem eq_zero_of_eval_eq_zero [Finite σ] (p : MvPolynomial σ K) (h : ∀ v : σ → K, eval v p = 0)
     (hp : p ∈ restrictDegree σ K (Fintype.card K - 1)) : p = 0 :=
   let p' : R σ K := ⟨p, hp⟩
   have : p' ∈ (evalᵢ σ K).ker := funext h
   show p'.1 = (0 : R σ K).1 from congr_arg _ <| by rwa [ker_evalₗ, mem_bot] at this 
 #align mv_polynomial.eq_zero_of_eval_eq_zero MvPolynomial.eq_zero_of_eval_eq_zero
+-/
 
 end MvPolynomial
 

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

@@ -71,7 +71,7 @@ variable [Fintype K] [Fintype σ]
 #print MvPolynomial.indicator /-
 /-- Over a field, this is the indicator function as an `mv_polynomial`. -/
 def indicator [CommRing K] (a : σ → K) : MvPolynomial σ K :=
-  ∏ n, 1 - (X n - C (a n)) ^ (Fintype.card K - 1)
+  ∏ n, (1 - (X n - C (a n)) ^ (Fintype.card K - 1))
 #align mv_polynomial.indicator MvPolynomial.indicator
 -/
 

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

@@ -233,7 +233,6 @@ theorem rank_R [Fintype σ] : Module.rank K (R σ K) = Fintype.card (σ → K) :
       (Equiv.arrowCongr (Equiv.refl σ) Fin.equivSubtype.symm).cardinal_eq
     _ = (#σ → K) := (Equiv.arrowCongr (Equiv.refl σ) (Fintype.equivFin K).symm).cardinal_eq
     _ = Fintype.card (σ → K) := Cardinal.mk_fintype _
-    
 #align mv_polynomial.rank_R MvPolynomial.rank_R
 
 instance [Finite σ] : FiniteDimensional K (R σ K) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/13361559d66b84f80b6d5a1c4a26aa5054766725

@@ -28,27 +28,27 @@ variable {σ : Type _}
 
 /-- A polynomial over the integers is divisible by `n : ℕ`
 if and only if it is zero over `zmod n`. -/
-theorem c_dvd_iff_zMod (n : ℕ) (φ : MvPolynomial σ ℤ) :
+theorem C_dvd_iff_zmod (n : ℕ) (φ : MvPolynomial σ ℤ) :
     C (n : ℤ) ∣ φ ↔ map (Int.castRingHom (ZMod n)) φ = 0 :=
   C_dvd_iff_map_hom_eq_zero _ _ (CharP.int_cast_eq_zero_iff (ZMod n) n) _
-#align mv_polynomial.C_dvd_iff_zmod MvPolynomial.c_dvd_iff_zMod
+#align mv_polynomial.C_dvd_iff_zmod MvPolynomial.C_dvd_iff_zmod
 
 section frobenius
 
 variable {p : ℕ} [Fact p.Prime]
 
-theorem frobenius_zMod (f : MvPolynomial σ (ZMod p)) : frobenius _ p f = expand p f :=
+theorem frobenius_zmod (f : MvPolynomial σ (ZMod p)) : frobenius _ p f = expand p f :=
   by
   apply induction_on f
   · intro a; rw [expand_C, frobenius_def, ← C_pow, ZMod.pow_card]
   · simp only [AlgHom.map_add, RingHom.map_add]; intro _ _ hf hg; rw [hf, hg]
   · simp only [expand_X, RingHom.map_mul, AlgHom.map_mul]
     intro _ _ hf; rw [hf, frobenius_def]
-#align mv_polynomial.frobenius_zmod MvPolynomial.frobenius_zMod
+#align mv_polynomial.frobenius_zmod MvPolynomial.frobenius_zmod
 
-theorem expand_zMod (f : MvPolynomial σ (ZMod p)) : expand p f = f ^ p :=
-  (frobenius_zMod _).symm
-#align mv_polynomial.expand_zmod MvPolynomial.expand_zMod
+theorem expand_zmod (f : MvPolynomial σ (ZMod p)) : expand p f = f ^ p :=
+  (frobenius_zmod _).symm
+#align mv_polynomial.expand_zmod MvPolynomial.expand_zmod
 
 end frobenius
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module field_theory.finite.polynomial
-! leanprover-community/mathlib commit 5aa3c1de9f3c642eac76e11071c852766f220fd0
+! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.FieldTheory.Finite.Basic
 
 /-!
 ## Polynomials over finite fields
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 -/
 
 
@@ -65,10 +68,12 @@ section Indicator
 
 variable [Fintype K] [Fintype σ]
 
+#print MvPolynomial.indicator /-
 /-- Over a field, this is the indicator function as an `mv_polynomial`. -/
 def indicator [CommRing K] (a : σ → K) : MvPolynomial σ K :=
   ∏ n, 1 - (X n - C (a n)) ^ (Fintype.card K - 1)
 #align mv_polynomial.indicator MvPolynomial.indicator
+-/
 
 section CommRing
 
@@ -95,6 +100,7 @@ theorem degrees_indicator (c : σ → K) :
   exact degrees_X' _
 #align mv_polynomial.degrees_indicator MvPolynomial.degrees_indicator
 
+#print MvPolynomial.indicator_mem_restrictDegree /-
 theorem indicator_mem_restrictDegree (c : σ → K) :
     indicator c ∈ restrictDegree σ K (Fintype.card K - 1) :=
   by
@@ -109,6 +115,7 @@ theorem indicator_mem_restrictDegree (c : σ → K) :
   · intro h; exact (h <| Finset.mem_univ _).elim
   · rw [Multiset.count_singleton_self, mul_one]
 #align mv_polynomial.indicator_mem_restrict_degree MvPolynomial.indicator_mem_restrictDegree
+-/
 
 end CommRing
 
@@ -130,6 +137,7 @@ section
 
 variable (K σ)
 
+#print MvPolynomial.evalₗ /-
 /-- `mv_polynomial.eval` as a `K`-linear map. -/
 @[simps]
 def evalₗ [CommSemiring K] : MvPolynomial σ K →ₗ[K] (σ → K) → K
@@ -138,6 +146,7 @@ def evalₗ [CommSemiring K] : MvPolynomial σ K →ₗ[K] (σ → K) → K
   map_add' p q := by ext x; rw [RingHom.map_add]; rfl
   map_smul' a p := by ext e; rw [smul_eq_C_mul, RingHom.map_mul, eval_C]; rfl
 #align mv_polynomial.evalₗ MvPolynomial.evalₗ
+-/
 
 end
 
@@ -172,42 +181,48 @@ universe u
 
 variable (σ : Type u) (K : Type u) [Fintype K]
 
-/- ./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler module[module] K -/
+/- ./././Mathport/Syntax/Translate/Command.lean:43:9: unsupported derive handler module[module] K -/
+#print MvPolynomial.R /-
 /-- The submodule of multivariate polynomials whose degree of each variable is strictly less
 than the cardinality of K. -/
 def R [CommRing K] : Type u :=
   restrictDegree σ K (Fintype.card K - 1)
 deriving AddCommGroup,
-  «./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler module[module] K»,
+  «./././Mathport/Syntax/Translate/Command.lean:43:9: unsupported derive handler module[module] K»,
   Inhabited
 #align mv_polynomial.R MvPolynomial.R
+-/
 
+#print MvPolynomial.evalᵢ /-
 /-- Evaluation in the `mv_polynomial.R` subtype. -/
 def evalᵢ [CommRing K] : R σ K →ₗ[K] (σ → K) → K :=
   (evalₗ K σ).comp (restrictDegree σ K (Fintype.card K - 1)).Subtype
 #align mv_polynomial.evalᵢ MvPolynomial.evalᵢ
+-/
 
 section CommRing
 
 variable [CommRing K]
 
+#print MvPolynomial.decidableRestrictDegree /-
 noncomputable instance decidableRestrictDegree (m : ℕ) :
-    DecidablePred (· ∈ { n : σ →₀ ℕ | ∀ i, n i ≤ m }) := by
+    DecidablePred (· ∈ {n : σ →₀ ℕ | ∀ i, n i ≤ m}) := by
   simp only [Set.mem_setOf_eq] <;> infer_instance
 #align mv_polynomial.decidable_restrict_degree MvPolynomial.decidableRestrictDegree
+-/
 
 end CommRing
 
 variable [Field K]
 
-theorem rank_r [Fintype σ] : Module.rank K (R σ K) = Fintype.card (σ → K) :=
+theorem rank_R [Fintype σ] : Module.rank K (R σ K) = Fintype.card (σ → K) :=
   calc
     Module.rank K (R σ K) =
-        Module.rank K (↥{ s : σ →₀ ℕ | ∀ n : σ, s n ≤ Fintype.card K - 1 } →₀ K) :=
+        Module.rank K (↥{s : σ →₀ ℕ | ∀ n : σ, s n ≤ Fintype.card K - 1} →₀ K) :=
       LinearEquiv.rank_eq
-        (Finsupp.supportedEquivFinsupp { s : σ →₀ ℕ | ∀ n : σ, s n ≤ Fintype.card K - 1 })
-    _ = (#{ s : σ →₀ ℕ | ∀ n : σ, s n ≤ Fintype.card K - 1 }) := by rw [rank_finsupp_self']
-    _ = (#{ s : σ → ℕ | ∀ n : σ, s n < Fintype.card K }) :=
+        (Finsupp.supportedEquivFinsupp {s : σ →₀ ℕ | ∀ n : σ, s n ≤ Fintype.card K - 1})
+    _ = (#{s : σ →₀ ℕ | ∀ n : σ, s n ≤ Fintype.card K - 1}) := by rw [rank_finsupp_self']
+    _ = (#{s : σ → ℕ | ∀ n : σ, s n < Fintype.card K}) :=
       by
       refine' Quotient.sound ⟨Equiv.subtypeEquiv Finsupp.equivFunOnFinite fun f => _⟩
       refine' forall_congr' fun n => le_tsub_iff_right _
@@ -219,7 +234,7 @@ theorem rank_r [Fintype σ] : Module.rank K (R σ K) = Fintype.card (σ → K) :
     _ = (#σ → K) := (Equiv.arrowCongr (Equiv.refl σ) (Fintype.equivFin K).symm).cardinal_eq
     _ = Fintype.card (σ → K) := Cardinal.mk_fintype _
     
-#align mv_polynomial.rank_R MvPolynomial.rank_r
+#align mv_polynomial.rank_R MvPolynomial.rank_R
 
 instance [Finite σ] : FiniteDimensional K (R σ K) :=
   by
@@ -229,9 +244,11 @@ instance [Finite σ] : FiniteDimensional K (R σ K) :=
       (is_noetherian.iff_rank_lt_aleph_0.mpr <| by
         simpa only [rank_R] using Cardinal.nat_lt_aleph0 (Fintype.card (σ → K)))
 
-theorem finrank_r [Fintype σ] : FiniteDimensional.finrank K (R σ K) = Fintype.card (σ → K) :=
-  FiniteDimensional.finrank_eq_of_rank_eq (rank_r σ K)
-#align mv_polynomial.finrank_R MvPolynomial.finrank_r
+#print MvPolynomial.finrank_R /-
+theorem finrank_R [Fintype σ] : FiniteDimensional.finrank K (R σ K) = Fintype.card (σ → K) :=
+  FiniteDimensional.finrank_eq_of_rank_eq (rank_R σ K)
+#align mv_polynomial.finrank_R MvPolynomial.finrank_R
+-/
 
 theorem range_evalᵢ [Finite σ] : (evalᵢ σ K).range = ⊤ :=
   by

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

@@ -116,7 +116,7 @@ variable [Field K]
 
 theorem eval_indicator_apply_eq_zero (a b : σ → K) (h : a ≠ b) : eval a (indicator b) = 0 :=
   by
-  obtain ⟨i, hi⟩ : ∃ i, a i ≠ b i := by rwa [(· ≠ ·), Function.funext_iff, not_forall] at h
+  obtain ⟨i, hi⟩ : ∃ i, a i ≠ b i := by rwa [(· ≠ ·), Function.funext_iff, not_forall] at h 
   simp only [indicator, map_prod, map_sub, map_one, map_pow, eval_X, eval_C, sub_self,
     Finset.prod_eq_zero_iff]
   refine' ⟨i, Finset.mem_univ _, _⟩
@@ -176,7 +176,8 @@ variable (σ : Type u) (K : Type u) [Fintype K]
 /-- The submodule of multivariate polynomials whose degree of each variable is strictly less
 than the cardinality of K. -/
 def R [CommRing K] : Type u :=
-  restrictDegree σ K (Fintype.card K - 1)deriving AddCommGroup,
+  restrictDegree σ K (Fintype.card K - 1)
+deriving AddCommGroup,
   «./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler module[module] K»,
   Inhabited
 #align mv_polynomial.R MvPolynomial.R
@@ -249,7 +250,7 @@ theorem eq_zero_of_eval_eq_zero [Finite σ] (p : MvPolynomial σ K) (h : ∀ v :
     (hp : p ∈ restrictDegree σ K (Fintype.card K - 1)) : p = 0 :=
   let p' : R σ K := ⟨p, hp⟩
   have : p' ∈ (evalᵢ σ K).ker := funext h
-  show p'.1 = (0 : R σ K).1 from congr_arg _ <| by rwa [ker_evalₗ, mem_bot] at this
+  show p'.1 = (0 : R σ K).1 from congr_arg _ <| by rwa [ker_evalₗ, mem_bot] at this 
 #align mv_polynomial.eq_zero_of_eval_eq_zero MvPolynomial.eq_zero_of_eval_eq_zero
 
 end MvPolynomial

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

@@ -55,7 +55,7 @@ namespace MvPolynomial
 
 noncomputable section
 
-open BigOperators Classical
+open scoped BigOperators Classical
 
 open Set LinearMap Submodule
 
@@ -164,7 +164,7 @@ end MvPolynomial
 
 namespace MvPolynomial
 
-open Classical Cardinal
+open scoped Classical Cardinal
 
 open LinearMap Submodule
 

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

@@ -37,14 +37,10 @@ variable {p : ℕ} [Fact p.Prime]
 theorem frobenius_zMod (f : MvPolynomial σ (ZMod p)) : frobenius _ p f = expand p f :=
   by
   apply induction_on f
-  · intro a
-    rw [expand_C, frobenius_def, ← C_pow, ZMod.pow_card]
-  · simp only [AlgHom.map_add, RingHom.map_add]
-    intro _ _ hf hg
-    rw [hf, hg]
+  · intro a; rw [expand_C, frobenius_def, ← C_pow, ZMod.pow_card]
+  · simp only [AlgHom.map_add, RingHom.map_add]; intro _ _ hf hg; rw [hf, hg]
   · simp only [expand_X, RingHom.map_mul, AlgHom.map_mul]
-    intro _ _ hf
-    rw [hf, frobenius_def]
+    intro _ _ hf; rw [hf, frobenius_def]
 #align mv_polynomial.frobenius_zmod MvPolynomial.frobenius_zMod
 
 theorem expand_zMod (f : MvPolynomial σ (ZMod p)) : expand p f = f ^ p :=
@@ -109,10 +105,8 @@ theorem indicator_mem_restrictDegree (c : σ → K) :
     AddMonoidHom.map_nsmul, Multiset.coe_countAddMonoidHom, nsmul_eq_mul, Nat.cast_id]
   trans
   refine' Finset.sum_eq_single n _ _
-  · intro b hb ne
-    rw [Multiset.count_singleton, if_neg Ne.symm, MulZeroClass.mul_zero]
-  · intro h
-    exact (h <| Finset.mem_univ _).elim
+  · intro b hb ne; rw [Multiset.count_singleton, if_neg Ne.symm, MulZeroClass.mul_zero]
+  · intro h; exact (h <| Finset.mem_univ _).elim
   · rw [Multiset.count_singleton_self, mul_one]
 #align mv_polynomial.indicator_mem_restrict_degree MvPolynomial.indicator_mem_restrictDegree
 
@@ -141,14 +135,8 @@ variable (K σ)
 def evalₗ [CommSemiring K] : MvPolynomial σ K →ₗ[K] (σ → K) → K
     where
   toFun p e := eval e p
-  map_add' p q := by
-    ext x
-    rw [RingHom.map_add]
-    rfl
-  map_smul' a p := by
-    ext e
-    rw [smul_eq_C_mul, RingHom.map_mul, eval_C]
-    rfl
+  map_add' p q := by ext x; rw [RingHom.map_add]; rfl
+  map_smul' a p := by ext e; rw [smul_eq_C_mul, RingHom.map_mul, eval_C]; rfl
 #align mv_polynomial.evalₗ MvPolynomial.evalₗ
 
 end

mathlib commit https://github.com/leanprover-community/mathlib/commit/5ec62c8106221a3f9160e4e4fcc3eed79fe213e9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module field_theory.finite.polynomial
-! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
+! leanprover-community/mathlib commit 5aa3c1de9f3c642eac76e11071c852766f220fd0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -217,8 +217,7 @@ theorem rank_r [Fintype σ] : Module.rank K (R σ K) = Fintype.card (σ → K) :
         Module.rank K (↥{ s : σ →₀ ℕ | ∀ n : σ, s n ≤ Fintype.card K - 1 } →₀ K) :=
       LinearEquiv.rank_eq
         (Finsupp.supportedEquivFinsupp { s : σ →₀ ℕ | ∀ n : σ, s n ≤ Fintype.card K - 1 })
-    _ = (#{ s : σ →₀ ℕ | ∀ n : σ, s n ≤ Fintype.card K - 1 }) := by
-      rw [Finsupp.rank_eq, rank_self, mul_one]
+    _ = (#{ s : σ →₀ ℕ | ∀ n : σ, s n ≤ Fintype.card K - 1 }) := by rw [rank_finsupp_self']
     _ = (#{ s : σ → ℕ | ∀ n : σ, s n < Fintype.card K }) :=
       by
       refine' Quotient.sound ⟨Equiv.subtypeEquiv Finsupp.equivFunOnFinite fun f => _⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module field_theory.finite.polynomial
-! leanprover-community/mathlib commit 5fd3186f1ec30a75d5f65732e3ce5e623382556f
+! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -211,14 +211,14 @@ end CommRing
 
 variable [Field K]
 
-theorem dim_r [Fintype σ] : Module.rank K (R σ K) = Fintype.card (σ → K) :=
+theorem rank_r [Fintype σ] : Module.rank K (R σ K) = Fintype.card (σ → K) :=
   calc
     Module.rank K (R σ K) =
         Module.rank K (↥{ s : σ →₀ ℕ | ∀ n : σ, s n ≤ Fintype.card K - 1 } →₀ K) :=
-      LinearEquiv.dim_eq
+      LinearEquiv.rank_eq
         (Finsupp.supportedEquivFinsupp { s : σ →₀ ℕ | ∀ n : σ, s n ≤ Fintype.card K - 1 })
     _ = (#{ s : σ →₀ ℕ | ∀ n : σ, s n ≤ Fintype.card K - 1 }) := by
-      rw [Finsupp.dim_eq, dim_self, mul_one]
+      rw [Finsupp.rank_eq, rank_self, mul_one]
     _ = (#{ s : σ → ℕ | ∀ n : σ, s n < Fintype.card K }) :=
       by
       refine' Quotient.sound ⟨Equiv.subtypeEquiv Finsupp.equivFunOnFinite fun f => _⟩
@@ -231,18 +231,18 @@ theorem dim_r [Fintype σ] : Module.rank K (R σ K) = Fintype.card (σ → K) :=
     _ = (#σ → K) := (Equiv.arrowCongr (Equiv.refl σ) (Fintype.equivFin K).symm).cardinal_eq
     _ = Fintype.card (σ → K) := Cardinal.mk_fintype _
     
-#align mv_polynomial.dim_R MvPolynomial.dim_r
+#align mv_polynomial.rank_R MvPolynomial.rank_r
 
 instance [Finite σ] : FiniteDimensional K (R σ K) :=
   by
   cases nonempty_fintype σ
   exact
     IsNoetherian.iff_fg.1
-      (is_noetherian.iff_dim_lt_aleph_0.mpr <| by
-        simpa only [dim_R] using Cardinal.nat_lt_aleph0 (Fintype.card (σ → K)))
+      (is_noetherian.iff_rank_lt_aleph_0.mpr <| by
+        simpa only [rank_R] using Cardinal.nat_lt_aleph0 (Fintype.card (σ → K)))
 
 theorem finrank_r [Fintype σ] : FiniteDimensional.finrank K (R σ K) = Fintype.card (σ → K) :=
-  FiniteDimensional.finrank_eq_of_dim_eq (dim_r σ K)
+  FiniteDimensional.finrank_eq_of_rank_eq (rank_r σ K)
 #align mv_polynomial.finrank_R MvPolynomial.finrank_r
 
 theorem range_evalᵢ [Finite σ] : (evalᵢ σ K).range = ⊤ :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd

@@ -26,8 +26,8 @@ variable {σ : Type _}
 /-- A polynomial over the integers is divisible by `n : ℕ`
 if and only if it is zero over `zmod n`. -/
 theorem c_dvd_iff_zMod (n : ℕ) (φ : MvPolynomial σ ℤ) :
-    c (n : ℤ) ∣ φ ↔ map (Int.castRingHom (ZMod n)) φ = 0 :=
-  c_dvd_iff_map_hom_eq_zero _ _ (CharP.int_cast_eq_zero_iff (ZMod n) n) _
+    C (n : ℤ) ∣ φ ↔ map (Int.castRingHom (ZMod n)) φ = 0 :=
+  C_dvd_iff_map_hom_eq_zero _ _ (CharP.int_cast_eq_zero_iff (ZMod n) n) _
 #align mv_polynomial.C_dvd_iff_zmod MvPolynomial.c_dvd_iff_zMod
 
 section frobenius
@@ -71,7 +71,7 @@ variable [Fintype K] [Fintype σ]
 
 /-- Over a field, this is the indicator function as an `mv_polynomial`. -/
 def indicator [CommRing K] (a : σ → K) : MvPolynomial σ K :=
-  ∏ n, 1 - (x n - c (a n)) ^ (Fintype.card K - 1)
+  ∏ n, 1 - (X n - C (a n)) ^ (Fintype.card K - 1)
 #align mv_polynomial.indicator MvPolynomial.indicator
 
 section CommRing

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -110,7 +110,7 @@ theorem indicator_mem_restrictDegree (c : σ → K) :
   trans
   refine' Finset.sum_eq_single n _ _
   · intro b hb ne
-    rw [Multiset.count_singleton, if_neg Ne.symm, mul_zero]
+    rw [Multiset.count_singleton, if_neg Ne.symm, MulZeroClass.mul_zero]
   · intro h
     exact (h <| Finset.mem_univ _).elim
   · rw [Multiset.count_singleton_self, mul_one]

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

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.

@@ -22,7 +22,7 @@ variable {σ : Type*}
 if and only if it is zero over `ZMod n`. -/
 theorem C_dvd_iff_zmod (n : ℕ) (φ : MvPolynomial σ ℤ) :
     C (n : ℤ) ∣ φ ↔ map (Int.castRingHom (ZMod n)) φ = 0 :=
-  C_dvd_iff_map_hom_eq_zero _ _ (CharP.int_cast_eq_zero_iff (ZMod n) n) _
+  C_dvd_iff_map_hom_eq_zero _ _ (CharP.intCast_eq_zero_iff (ZMod n) n) _
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.C_dvd_iff_zmod MvPolynomial.C_dvd_iff_zmod
 

A mix of various changes; generated with a script and manually tweaked.

@@ -133,7 +133,7 @@ def evalₗ [CommSemiring K] : MvPolynomial σ K →ₗ[K] (σ → K) → K wher
 variable [Field K] [Fintype K] [Finite σ]
 
 -- Porting note: `K` and `σ` were implicit in mathlib3, even if they were declared via
--- `variables (K σ)` (I don't understand why). They are now explicit, as expected.
+-- `variable (K σ)` (I don't understand why). They are now explicit, as expected.
 theorem map_restrict_dom_evalₗ : (restrictDegree σ K (Fintype.card K - 1)).map (evalₗ K σ) = ⊤ := by
   cases nonempty_fintype σ
   refine' top_unique (SetLike.le_def.2 fun e _ => mem_map.2 _)

Polynomial and MvPolynomial are algebraic objects, hence should be under Algebra (or at least not under Data)

@@ -3,7 +3,7 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import Mathlib.Data.MvPolynomial.Expand
+import Mathlib.Algebra.MvPolynomial.Expand
 import Mathlib.FieldTheory.Finite.Basic
 import Mathlib.RingTheory.MvPolynomial.Basic
 

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -166,7 +166,7 @@ universe u
 
 variable (σ : Type u) (K : Type u) [Fintype K]
 
---Porting note: `@[derive [add_comm_group, module K, inhabited]]` done by hand.
+-- Porting note: `@[derive [add_comm_group, module K, inhabited]]` done by hand.
 /-- The submodule of multivariate polynomials whose degree of each variable is strictly less
 than the cardinality of K. -/
 def R [CommRing K] : Type u :=
@@ -239,7 +239,7 @@ theorem range_evalᵢ [Finite σ] : range (evalᵢ σ K) = ⊤ := by
   exact map_restrict_dom_evalₗ K σ
 #align mv_polynomial.range_evalᵢ MvPolynomial.range_evalᵢ
 
---Porting note: was `(evalᵢ σ K).ker`.
+-- Porting note: was `(evalᵢ σ K).ker`.
 theorem ker_evalₗ [Finite σ] : ker (evalᵢ σ K) = ⊥ := by
   cases nonempty_fintype σ
   refine' (ker_eq_bot_iff_range_eq_top_of_finrank_eq_finrank _).mpr (range_evalᵢ σ K)

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

From LeanAPAP

@@ -73,7 +73,7 @@ theorem eval_indicator_apply_eq_one (a : σ → K) : eval a (indicator a) = 1 :=
   nontriviality
   have : 0 < Fintype.card K - 1 := tsub_pos_of_lt Fintype.one_lt_card
   simp only [indicator, map_prod, map_sub, map_one, map_pow, eval_X, eval_C, sub_self,
-    zero_pow this, sub_zero, Finset.prod_const_one]
+    zero_pow this.ne', sub_zero, Finset.prod_const_one]
 #align mv_polynomial.eval_indicator_apply_eq_one MvPolynomial.eval_indicator_apply_eq_one
 
 theorem degrees_indicator (c : σ → K) :

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

Renames

Algebra.GroupPower.Order

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

Algebra.GroupPower.CovariantClass

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

Data.Nat.Pow

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

Lemmas added

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

Lemmas removed

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

Other changes

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

@@ -82,7 +82,7 @@ theorem degrees_indicator (c : σ → K) :
   refine' le_trans (degrees_prod _ _) (Finset.sum_le_sum fun s _ => _)
   refine' le_trans (degrees_sub _ _) _
   rw [degrees_one, ← bot_eq_zero, bot_sup_eq]
-  refine' le_trans (degrees_pow _ _) (nsmul_le_nsmul_of_le_right _ _)
+  refine' le_trans (degrees_pow _ _) (nsmul_le_nsmul_right _ _)
   refine' le_trans (degrees_sub _ _) _
   rw [degrees_C, ← bot_eq_zero, sup_bot_eq]
   exact degrees_X' _

@@ -93,7 +93,7 @@ theorem indicator_mem_restrictDegree (c : σ → K) :
   rw [mem_restrictDegree_iff_sup, indicator]
   intro n
   refine' le_trans (Multiset.count_le_of_le _ <| degrees_indicator _) (le_of_eq _)
-  simp_rw [← Multiset.coe_countAddMonoidHom, (Multiset.countAddMonoidHom n).map_sum,
+  simp_rw [← Multiset.coe_countAddMonoidHom, map_sum,
     AddMonoidHom.map_nsmul, Multiset.coe_countAddMonoidHom, nsmul_eq_mul, Nat.cast_id]
   trans
   refine' Finset.sum_eq_single n _ _

This reduces the file from ~2600 lines to ~1600 lines.

Co-authored-by: Vierkantor <vierkantor@vierkantor.com> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

@@ -3,11 +3,9 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import Mathlib.LinearAlgebra.FiniteDimensional
-import Mathlib.LinearAlgebra.Basic
-import Mathlib.RingTheory.MvPolynomial.Basic
 import Mathlib.Data.MvPolynomial.Expand
 import Mathlib.FieldTheory.Finite.Basic
+import Mathlib.RingTheory.MvPolynomial.Basic
 
 #align_import field_theory.finite.polynomial from "leanprover-community/mathlib"@"5aa3c1de9f3c642eac76e11071c852766f220fd0"
 

@@ -146,9 +146,9 @@ theorem map_restrict_dom_evalₗ : (restrictDegree σ K (Fintype.card K - 1)).ma
       map_smul]
     simp only [evalₗ_apply]
     trans
-    refine' Finset.sum_eq_single n (fun b _ h => _) _
-    · rw [eval_indicator_apply_eq_zero _ _ h.symm, smul_zero]
-    · exact fun h => (h <| Finset.mem_univ n).elim
+    · refine' Finset.sum_eq_single n (fun b _ h => _) _
+      · rw [eval_indicator_apply_eq_zero _ _ h.symm, smul_zero]
+      · exact fun h => (h <| Finset.mem_univ n).elim
     · rw [eval_indicator_apply_eq_one, smul_eq_mul, mul_one]
 #align mv_polynomial.map_restrict_dom_evalₗ MvPolynomial.map_restrict_dom_evalₗ
 

Also _root_.map_smul when in the neighbourhood.

@@ -142,8 +142,8 @@ theorem map_restrict_dom_evalₗ : (restrictDegree σ K (Fintype.card K - 1)).ma
   refine' ⟨∑ n : σ → K, e n • indicator n, _, _⟩
   · exact sum_mem fun c _ => smul_mem _ _ (indicator_mem_restrictDegree _)
   · ext n
-    simp only [LinearMap.map_sum, @Finset.sum_apply (σ → K) (fun _ => K) _ _ _ _ _, Pi.smul_apply,
-      LinearMap.map_smul]
+    simp only [_root_.map_sum, @Finset.sum_apply (σ → K) (fun _ => K) _ _ _ _ _, Pi.smul_apply,
+      map_smul]
     simp only [evalₗ_apply]
     trans
     refine' Finset.sum_eq_single n (fun b _ h => _) _

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

This has nice performance benefits.

@@ -18,7 +18,7 @@ import Mathlib.FieldTheory.Finite.Basic
 
 namespace MvPolynomial
 
-variable {σ : Type _}
+variable {σ : Type*}
 
 /-- A polynomial over the integers is divisible by `n : ℕ`
 if and only if it is zero over `ZMod n`. -/
@@ -56,7 +56,7 @@ open scoped BigOperators Classical
 
 open Set LinearMap Submodule
 
-variable {K : Type _} {σ : Type _}
+variable {K : Type*} {σ : Type*}
 
 section Indicator
 

• 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) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module field_theory.finite.polynomial
-! leanprover-community/mathlib commit 5aa3c1de9f3c642eac76e11071c852766f220fd0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.FiniteDimensional
 import Mathlib.LinearAlgebra.Basic
@@ -14,6 +9,8 @@ import Mathlib.RingTheory.MvPolynomial.Basic
 import Mathlib.Data.MvPolynomial.Expand
 import Mathlib.FieldTheory.Finite.Basic
 
+#align_import field_theory.finite.polynomial from "leanprover-community/mathlib"@"5aa3c1de9f3c642eac76e11071c852766f220fd0"
+
 /-!
 ## Polynomials over finite fields
 -/

@@ -212,16 +212,16 @@ theorem rank_R [Fintype σ] : Module.rank K (R σ K) = Fintype.card (σ → K) :
         Module.rank K (↥{ s : σ →₀ ℕ | ∀ n : σ, s n ≤ Fintype.card K - 1 } →₀ K) :=
       LinearEquiv.rank_eq
         (Finsupp.supportedEquivFinsupp { s : σ →₀ ℕ | ∀ n : σ, s n ≤ Fintype.card K - 1 })
-    _ = (#{ s : σ →₀ ℕ | ∀ n : σ, s n ≤ Fintype.card K - 1 }) := by rw [rank_finsupp_self']
-    _ = (#{ s : σ → ℕ | ∀ n : σ, s n < Fintype.card K }) := by
+    _ = #{ s : σ →₀ ℕ | ∀ n : σ, s n ≤ Fintype.card K - 1 } := by rw [rank_finsupp_self']
+    _ = #{ s : σ → ℕ | ∀ n : σ, s n < Fintype.card K } := by
       refine' Quotient.sound ⟨Equiv.subtypeEquiv Finsupp.equivFunOnFinite fun f => _⟩
       refine' forall_congr' fun n => le_tsub_iff_right _
       exact Fintype.card_pos_iff.2 ⟨0⟩
-    _ = (#σ → { n // n < Fintype.card K }) :=
+    _ = #(σ → { n // n < Fintype.card K }) :=
       (@Equiv.subtypePiEquivPi σ (fun _ => ℕ) fun s n => n < Fintype.card K).cardinal_eq
-    _ = (#σ → Fin (Fintype.card K)) :=
+    _ = #(σ → Fin (Fintype.card K)) :=
       (Equiv.arrowCongr (Equiv.refl σ) Fin.equivSubtype.symm).cardinal_eq
-    _ = (#σ → K) := (Equiv.arrowCongr (Equiv.refl σ) (Fintype.equivFin K).symm).cardinal_eq
+    _ = #(σ → K) := (Equiv.arrowCongr (Equiv.refl σ) (Fintype.equivFin K).symm).cardinal_eq
     _ = Fintype.card (σ → K) := Cardinal.mk_fintype _
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.rank_R MvPolynomial.rank_R

@@ -25,27 +25,27 @@ variable {σ : Type _}
 
 /-- A polynomial over the integers is divisible by `n : ℕ`
 if and only if it is zero over `ZMod n`. -/
-theorem c_dvd_iff_zMod (n : ℕ) (φ : MvPolynomial σ ℤ) :
+theorem C_dvd_iff_zmod (n : ℕ) (φ : MvPolynomial σ ℤ) :
     C (n : ℤ) ∣ φ ↔ map (Int.castRingHom (ZMod n)) φ = 0 :=
   C_dvd_iff_map_hom_eq_zero _ _ (CharP.int_cast_eq_zero_iff (ZMod n) n) _
 set_option linter.uppercaseLean3 false in
-#align mv_polynomial.C_dvd_iff_zmod MvPolynomial.c_dvd_iff_zMod
+#align mv_polynomial.C_dvd_iff_zmod MvPolynomial.C_dvd_iff_zmod
 
 section frobenius
 
 variable {p : ℕ} [Fact p.Prime]
 
-theorem frobenius_zMod (f : MvPolynomial σ (ZMod p)) : frobenius _ p f = expand p f := by
+theorem frobenius_zmod (f : MvPolynomial σ (ZMod p)) : frobenius _ p f = expand p f := by
   apply induction_on f
   · intro a; rw [expand_C, frobenius_def, ← C_pow, ZMod.pow_card]
   · simp only [AlgHom.map_add, RingHom.map_add]; intro _ _ hf hg; rw [hf, hg]
   · simp only [expand_X, RingHom.map_mul, AlgHom.map_mul]
     intro _ _ hf; rw [hf, frobenius_def]
-#align mv_polynomial.frobenius_zmod MvPolynomial.frobenius_zMod
+#align mv_polynomial.frobenius_zmod MvPolynomial.frobenius_zmod
 
-theorem expand_zMod (f : MvPolynomial σ (ZMod p)) : expand p f = f ^ p :=
-  (frobenius_zMod _).symm
-#align mv_polynomial.expand_zmod MvPolynomial.expand_zMod
+theorem expand_zmod (f : MvPolynomial σ (ZMod p)) : expand p f = f ^ p :=
+  (frobenius_zmod _).symm
+#align mv_polynomial.expand_zmod MvPolynomial.expand_zmod
 
 end frobenius