field_theory.separable_degree ⟷ Mathlib.RingTheory.Polynomial.SeparableDegree

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

@@ -145,7 +145,7 @@ theorem contraction_degree_eq_or_insep [hq : NeZero q] [CharP F q] (g g' : F[X])
   wlog hm : m ≤ m'
   · exact (this g' g m' m h_expand.symm hg' hg (le_of_not_le hm)).symm
   obtain ⟨s, rfl⟩ := exists_add_of_le hm
-  rw [pow_add, expand_mul, expand_inj (pow_pos (NeZero.pos q) m)] at h_expand 
+  rw [pow_add, expand_mul, expand_inj (pow_pos (NeZero.pos q) m)] at h_expand
   subst h_expand
   rcases is_unit_or_eq_zero_of_separable_expand q s (NeZero.pos q) hg with (h | rfl)
   · rw [nat_degree_expand, nat_degree_eq_zero_of_is_unit h, MulZeroClass.zero_mul]
@@ -160,7 +160,7 @@ theorem IsSeparableContraction.degree_eq [hF : ExpChar F q] (g : F[X])
   by
   cases hF
   · rcases hg with ⟨g, m, hm⟩
-    rw [one_pow, expand_one] at hm 
+    rw [one_pow, expand_one] at hm
     rw [hf.eq_degree]
     rw [hm]
   · rcases hg with ⟨hg, m, hm⟩

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

@@ -123,17 +123,17 @@ variable {F : Type _} [Field F]
 
 variable (q : ℕ) {f : F[X]} (hf : HasSeparableContraction q f)
 
-#print Polynomial.Irreducible.hasSeparableContraction /-
+#print Irreducible.hasSeparableContraction /-
 /-- Every irreducible polynomial can be contracted to a separable polynomial.
 https://stacks.math.columbia.edu/tag/09H0 -/
-theorem Polynomial.Irreducible.hasSeparableContraction (q : ℕ) [hF : ExpChar F q] (f : F[X])
+theorem Irreducible.hasSeparableContraction (q : ℕ) [hF : ExpChar F q] (f : F[X])
     (irred : Irreducible f) : HasSeparableContraction q f :=
   by
   cases hF
   · exact ⟨f, irred.separable, ⟨0, by rw [pow_zero, expand_one]⟩⟩
   · rcases exists_separable_of_irreducible q irred ‹q.prime›.NeZero with ⟨n, g, hgs, hge⟩
     exact ⟨g, hgs, n, hge⟩
-#align irreducible.has_separable_contraction Polynomial.Irreducible.hasSeparableContraction
+#align irreducible.has_separable_contraction Irreducible.hasSeparableContraction
 -/
 
 #print Polynomial.contraction_degree_eq_or_insep /-

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

@@ -3,9 +3,9 @@ Copyright (c) 2021 Jakob Scholbach. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jakob Scholbach
 -/
-import Mathbin.Algebra.Algebra.Basic
-import Mathbin.Algebra.CharP.ExpChar
-import Mathbin.FieldTheory.Separable
+import Algebra.Algebra.Basic
+import Algebra.CharP.ExpChar
+import FieldTheory.Separable
 
 #align_import field_theory.separable_degree from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Jakob Scholbach. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jakob Scholbach
-
-! This file was ported from Lean 3 source module field_theory.separable_degree
-! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Algebra.Basic
 import Mathbin.Algebra.CharP.ExpChar
 import Mathbin.FieldTheory.Separable
 
+#align_import field_theory.separable_degree from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
+
 /-!
 
 # Separable degree

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

@@ -84,6 +84,7 @@ def HasSeparableContraction.degree : ℕ :=
 #align polynomial.has_separable_contraction.degree Polynomial.HasSeparableContraction.degree
 -/
 
+#print Polynomial.IsSeparableContraction.dvd_degree' /-
 /-- The separable degree divides the degree, in function of the exponential characteristic of F. -/
 theorem IsSeparableContraction.dvd_degree' {g} (hf : IsSeparableContraction q f g) :
     ∃ m : ℕ, g.natDegree * q ^ m = f.natDegree :=
@@ -92,6 +93,7 @@ theorem IsSeparableContraction.dvd_degree' {g} (hf : IsSeparableContraction q f
   use m
   rw [nat_degree_expand]
 #align polynomial.is_separable_contraction.dvd_degree' Polynomial.IsSeparableContraction.dvd_degree'
+-/
 
 #print Polynomial.HasSeparableContraction.dvd_degree' /-
 theorem HasSeparableContraction.dvd_degree' : ∃ m : ℕ, hf.degree * q ^ m = f.natDegree :=
@@ -124,6 +126,7 @@ variable {F : Type _} [Field F]
 
 variable (q : ℕ) {f : F[X]} (hf : HasSeparableContraction q f)
 
+#print Polynomial.Irreducible.hasSeparableContraction /-
 /-- Every irreducible polynomial can be contracted to a separable polynomial.
 https://stacks.math.columbia.edu/tag/09H0 -/
 theorem Polynomial.Irreducible.hasSeparableContraction (q : ℕ) [hF : ExpChar F q] (f : F[X])
@@ -134,7 +137,9 @@ theorem Polynomial.Irreducible.hasSeparableContraction (q : ℕ) [hF : ExpChar F
   · rcases exists_separable_of_irreducible q irred ‹q.prime›.NeZero with ⟨n, g, hgs, hge⟩
     exact ⟨g, hgs, n, hge⟩
 #align irreducible.has_separable_contraction Polynomial.Irreducible.hasSeparableContraction
+-/
 
+#print Polynomial.contraction_degree_eq_or_insep /-
 /-- If two expansions (along the positive characteristic) of two separable polynomials `g` and `g'`
 agree, then they have the same degree. -/
 theorem contraction_degree_eq_or_insep [hq : NeZero q] [CharP F q] (g g' : F[X]) (m m' : ℕ)
@@ -149,6 +154,7 @@ theorem contraction_degree_eq_or_insep [hq : NeZero q] [CharP F q] (g g' : F[X])
   · rw [nat_degree_expand, nat_degree_eq_zero_of_is_unit h, MulZeroClass.zero_mul]
   · rw [nat_degree_expand, pow_zero, mul_one]
 #align polynomial.contraction_degree_eq_or_insep Polynomial.contraction_degree_eq_or_insep
+-/
 
 #print Polynomial.IsSeparableContraction.degree_eq /-
 /-- The separable degree equals the degree of any separable contraction, i.e., it is unique. -/

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

@@ -143,7 +143,7 @@ theorem contraction_degree_eq_or_insep [hq : NeZero q] [CharP F q] (g g' : F[X])
   wlog hm : m ≤ m'
   · exact (this g' g m' m h_expand.symm hg' hg (le_of_not_le hm)).symm
   obtain ⟨s, rfl⟩ := exists_add_of_le hm
-  rw [pow_add, expand_mul, expand_inj (pow_pos (NeZero.pos q) m)] at h_expand
+  rw [pow_add, expand_mul, expand_inj (pow_pos (NeZero.pos q) m)] at h_expand 
   subst h_expand
   rcases is_unit_or_eq_zero_of_separable_expand q s (NeZero.pos q) hg with (h | rfl)
   · rw [nat_degree_expand, nat_degree_eq_zero_of_is_unit h, MulZeroClass.zero_mul]
@@ -157,7 +157,7 @@ theorem IsSeparableContraction.degree_eq [hF : ExpChar F q] (g : F[X])
   by
   cases hF
   · rcases hg with ⟨g, m, hm⟩
-    rw [one_pow, expand_one] at hm
+    rw [one_pow, expand_one] at hm 
     rw [hf.eq_degree]
     rw [hm]
   · rcases hg with ⟨hg, m, hm⟩

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

@@ -47,7 +47,7 @@ namespace Polynomial
 
 noncomputable section
 
-open Classical Polynomial
+open scoped Classical Polynomial
 
 section CommSemiring
 

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

@@ -84,12 +84,6 @@ def HasSeparableContraction.degree : ℕ :=
 #align polynomial.has_separable_contraction.degree Polynomial.HasSeparableContraction.degree
 -/
 
-/- warning: polynomial.is_separable_contraction.dvd_degree' -> Polynomial.IsSeparableContraction.dvd_degree' is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : CommSemiring.{u1} F] {q : Nat} {f : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F _inst_1)} {g : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F _inst_1)}, (Polynomial.IsSeparableContraction.{u1} F _inst_1 q f g) -> (Exists.{1} Nat (fun (m : Nat) => Eq.{1} Nat (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat Nat.hasMul) (Polynomial.natDegree.{u1} F (CommSemiring.toSemiring.{u1} F _inst_1) g) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) q m)) (Polynomial.natDegree.{u1} F (CommSemiring.toSemiring.{u1} F _inst_1) f)))
-but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : CommSemiring.{u1} F] {q : Nat} {f : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F _inst_1)}, (Polynomial.HasSeparableContraction.{u1} F _inst_1 q f) -> (forall {hf : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F _inst_1)}, (Polynomial.IsSeparableContraction.{u1} F _inst_1 q f hf) -> (Exists.{1} Nat (fun (m : Nat) => Eq.{1} Nat (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) (Polynomial.natDegree.{u1} F (CommSemiring.toSemiring.{u1} F _inst_1) hf) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) q m)) (Polynomial.natDegree.{u1} F (CommSemiring.toSemiring.{u1} F _inst_1) f))))
-Case conversion may be inaccurate. Consider using '#align polynomial.is_separable_contraction.dvd_degree' Polynomial.IsSeparableContraction.dvd_degree'ₓ'. -/
 /-- The separable degree divides the degree, in function of the exponential characteristic of F. -/
 theorem IsSeparableContraction.dvd_degree' {g} (hf : IsSeparableContraction q f g) :
     ∃ m : ℕ, g.natDegree * q ^ m = f.natDegree :=
@@ -130,12 +124,6 @@ variable {F : Type _} [Field F]
 
 variable (q : ℕ) {f : F[X]} (hf : HasSeparableContraction q f)
 
-/- warning: irreducible.has_separable_contraction -> Polynomial.Irreducible.hasSeparableContraction is a dubious translation:
-lean 3 declaration is
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (q : Nat) [hF : ExpChar.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) q] (f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))), (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) -> (Polynomial.HasSeparableContraction.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) q f)
-but is expected to have type
-  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (q : Nat) [hF : ExpChar.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) q] (f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))), (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (Polynomial.HasSeparableContraction.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) q f)
-Case conversion may be inaccurate. Consider using '#align irreducible.has_separable_contraction Polynomial.Irreducible.hasSeparableContractionₓ'. -/
 /-- Every irreducible polynomial can be contracted to a separable polynomial.
 https://stacks.math.columbia.edu/tag/09H0 -/
 theorem Polynomial.Irreducible.hasSeparableContraction (q : ℕ) [hF : ExpChar F q] (f : F[X])
@@ -147,9 +135,6 @@ theorem Polynomial.Irreducible.hasSeparableContraction (q : ℕ) [hF : ExpChar F
     exact ⟨g, hgs, n, hge⟩
 #align irreducible.has_separable_contraction Polynomial.Irreducible.hasSeparableContraction
 
-/- warning: polynomial.contraction_degree_eq_or_insep -> Polynomial.contraction_degree_eq_or_insep is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.contraction_degree_eq_or_insep Polynomial.contraction_degree_eq_or_insepₓ'. -/
 /-- If two expansions (along the positive characteristic) of two separable polynomials `g` and `g'`
 agree, then they have the same degree. -/
 theorem contraction_degree_eq_or_insep [hq : NeZero q] [CharP F q] (g g' : F[X]) (m m' : ℕ)

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

@@ -181,8 +181,7 @@ theorem IsSeparableContraction.degree_eq [hF : ExpChar F q] (g : F[X])
     haveI : Fact q.prime := fact_iff.2 hF_hprime
     apply contraction_degree_eq_or_insep q g g' m m'
     rw [hm, hm']
-    exact hg
-    exact (Classical.choose_spec hf).1
+    exact hg; exact (Classical.choose_spec hf).1
 #align polynomial.is_separable_contraction.degree_eq Polynomial.IsSeparableContraction.degree_eq
 -/
 

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

@@ -148,10 +148,7 @@ theorem Polynomial.Irreducible.hasSeparableContraction (q : ℕ) [hF : ExpChar F
 #align irreducible.has_separable_contraction Polynomial.Irreducible.hasSeparableContraction
 
 /- warning: polynomial.contraction_degree_eq_or_insep -> Polynomial.contraction_degree_eq_or_insep is a dubious translation:
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(CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F 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(Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} 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F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F 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(Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) q m')) g')) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g') -> (Eq.{1} Nat (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) g) (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) g'))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.contraction_degree_eq_or_insep Polynomial.contraction_degree_eq_or_insepₓ'. -/
 /-- If two expansions (along the positive characteristic) of two separable polynomials `g` and `g'`
 agree, then they have the same degree. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/e1a18cad9cd462973d760af7de36b05776b8811c

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jakob Scholbach
 
 ! This file was ported from Lean 3 source module field_theory.separable_degree
-! leanprover-community/mathlib commit d11893b411025250c8e61ff2f12ccbd7ee35ab15
+! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
 ! 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.Separable
 
 # Separable degree
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains basics about the separable degree of a polynomial.
 
 ## Main results

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

@@ -50,29 +50,43 @@ section CommSemiring
 
 variable {F : Type _} [CommSemiring F] (q : ℕ)
 
+#print Polynomial.IsSeparableContraction /-
 /-- A separable contraction of a polynomial `f` is a separable polynomial `g` such that
 `g(x^(q^m)) = f(x)` for some `m : ℕ`.-/
 def IsSeparableContraction (f : F[X]) (g : F[X]) : Prop :=
   g.Separable ∧ ∃ m : ℕ, expand F (q ^ m) g = f
 #align polynomial.is_separable_contraction Polynomial.IsSeparableContraction
+-/
 
+#print Polynomial.HasSeparableContraction /-
 /-- The condition of having a separable contration. -/
 def HasSeparableContraction (f : F[X]) : Prop :=
   ∃ g : F[X], IsSeparableContraction q f g
 #align polynomial.has_separable_contraction Polynomial.HasSeparableContraction
+-/
 
 variable {q} {f : F[X]} (hf : HasSeparableContraction q f)
 
+#print Polynomial.HasSeparableContraction.contraction /-
 /-- A choice of a separable contraction. -/
 def HasSeparableContraction.contraction : F[X] :=
   Classical.choose hf
 #align polynomial.has_separable_contraction.contraction Polynomial.HasSeparableContraction.contraction
+-/
 
+#print Polynomial.HasSeparableContraction.degree /-
 /-- The separable degree of a polynomial is the degree of a given separable contraction. -/
 def HasSeparableContraction.degree : ℕ :=
   hf.contraction.natDegree
 #align polynomial.has_separable_contraction.degree Polynomial.HasSeparableContraction.degree
+-/
 
+/- warning: polynomial.is_separable_contraction.dvd_degree' -> Polynomial.IsSeparableContraction.dvd_degree' is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : CommSemiring.{u1} F] {q : Nat} {f : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F _inst_1)} {g : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F _inst_1)}, (Polynomial.IsSeparableContraction.{u1} F _inst_1 q f g) -> (Exists.{1} Nat (fun (m : Nat) => Eq.{1} Nat (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat Nat.hasMul) (Polynomial.natDegree.{u1} F (CommSemiring.toSemiring.{u1} F _inst_1) g) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) q m)) (Polynomial.natDegree.{u1} F (CommSemiring.toSemiring.{u1} F _inst_1) f)))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : CommSemiring.{u1} F] {q : Nat} {f : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F _inst_1)}, (Polynomial.HasSeparableContraction.{u1} F _inst_1 q f) -> (forall {hf : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F _inst_1)}, (Polynomial.IsSeparableContraction.{u1} F _inst_1 q f hf) -> (Exists.{1} Nat (fun (m : Nat) => Eq.{1} Nat (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) (Polynomial.natDegree.{u1} F (CommSemiring.toSemiring.{u1} F _inst_1) hf) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) q m)) (Polynomial.natDegree.{u1} F (CommSemiring.toSemiring.{u1} F _inst_1) f))))
+Case conversion may be inaccurate. Consider using '#align polynomial.is_separable_contraction.dvd_degree' Polynomial.IsSeparableContraction.dvd_degree'ₓ'. -/
 /-- The separable degree divides the degree, in function of the exponential characteristic of F. -/
 theorem IsSeparableContraction.dvd_degree' {g} (hf : IsSeparableContraction q f g) :
     ∃ m : ℕ, g.natDegree * q ^ m = f.natDegree :=
@@ -82,22 +96,28 @@ theorem IsSeparableContraction.dvd_degree' {g} (hf : IsSeparableContraction q f
   rw [nat_degree_expand]
 #align polynomial.is_separable_contraction.dvd_degree' Polynomial.IsSeparableContraction.dvd_degree'
 
+#print Polynomial.HasSeparableContraction.dvd_degree' /-
 theorem HasSeparableContraction.dvd_degree' : ∃ m : ℕ, hf.degree * q ^ m = f.natDegree :=
   (Classical.choose_spec hf).dvd_degree'
 #align polynomial.has_separable_contraction.dvd_degree' Polynomial.HasSeparableContraction.dvd_degree'
+-/
 
+#print Polynomial.HasSeparableContraction.dvd_degree /-
 /-- The separable degree divides the degree. -/
 theorem HasSeparableContraction.dvd_degree : hf.degree ∣ f.natDegree :=
   let ⟨a, ha⟩ := hf.dvd_degree'
   Dvd.intro (q ^ a) ha
 #align polynomial.has_separable_contraction.dvd_degree Polynomial.HasSeparableContraction.dvd_degree
+-/
 
+#print Polynomial.HasSeparableContraction.eq_degree /-
 /-- In exponential characteristic one, the separable degree equals the degree. -/
 theorem HasSeparableContraction.eq_degree {f : F[X]} (hf : HasSeparableContraction 1 f) :
     hf.degree = f.natDegree := by
   let ⟨a, ha⟩ := hf.dvd_degree'
   rw [← ha, one_pow a, mul_one]
 #align polynomial.has_separable_contraction.eq_degree Polynomial.HasSeparableContraction.eq_degree
+-/
 
 end CommSemiring
 
@@ -107,17 +127,29 @@ variable {F : Type _} [Field F]
 
 variable (q : ℕ) {f : F[X]} (hf : HasSeparableContraction q f)
 
+/- warning: irreducible.has_separable_contraction -> Polynomial.Irreducible.hasSeparableContraction is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (q : Nat) [hF : ExpChar.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) q] (f : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))), (Irreducible.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Ring.toMonoid.{u1} (Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (Polynomial.ring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) f) -> (Polynomial.HasSeparableContraction.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) q f)
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (q : Nat) [hF : ExpChar.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) q] (f : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))), (Irreducible.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) f) -> (Polynomial.HasSeparableContraction.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) q f)
+Case conversion may be inaccurate. Consider using '#align irreducible.has_separable_contraction Polynomial.Irreducible.hasSeparableContractionₓ'. -/
 /-- Every irreducible polynomial can be contracted to a separable polynomial.
 https://stacks.math.columbia.edu/tag/09H0 -/
-theorem Irreducible.hasSeparableContraction (q : ℕ) [hF : ExpChar F q] (f : F[X])
+theorem Polynomial.Irreducible.hasSeparableContraction (q : ℕ) [hF : ExpChar F q] (f : F[X])
     (irred : Irreducible f) : HasSeparableContraction q f :=
   by
   cases hF
   · exact ⟨f, irred.separable, ⟨0, by rw [pow_zero, expand_one]⟩⟩
   · rcases exists_separable_of_irreducible q irred ‹q.prime›.NeZero with ⟨n, g, hgs, hge⟩
     exact ⟨g, hgs, n, hge⟩
-#align irreducible.has_separable_contraction Irreducible.hasSeparableContraction
-
+#align irreducible.has_separable_contraction Polynomial.Irreducible.hasSeparableContraction
+
+/- warning: polynomial.contraction_degree_eq_or_insep -> Polynomial.contraction_degree_eq_or_insep is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (q : Nat) [hq : NeZero.{0} Nat Nat.hasZero q] [_inst_2 : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (AddCommGroupWithOne.toAddGroupWithOne.{u1} F (Ring.toAddCommGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))) q] (g : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (g' : Polynomial.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (m : Nat) (m' : Nat), (Eq.{succ u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (coeFn.{succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F 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(Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) q m)) g) (coeFn.{succ u1, succ u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} 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F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) => (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) -> (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) ([anonymous].{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) q m')) g')) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g') -> (Eq.{1} Nat (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) g) (Polynomial.natDegree.{u1} F (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) g'))
+but is expected to have type
+  forall {F : Type.{u1}} [_inst_1 : Field.{u1} F] (q : Nat) [hq : NeZero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) q] [_inst_2 : CharP.{u1} F (AddGroupWithOne.toAddMonoidWithOne.{u1} F (Ring.toAddGroupWithOne.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) q] (g : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (g' : Polynomial.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (m : Nat) (m' : Nat), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) => Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) g) (FunLike.coe.{succ u1, succ u1, succ u1} 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_inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F 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F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (SMulZeroClass.toSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toZero.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulAction.toDistribSMul.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (MonoidWithZero.toMonoid.{u1} F (Semiring.toMonoidWithZero.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (Module.toDistribMulAction.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) (Algebra.toModule.{u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (AlgHom.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))) (AlgHom.algHomClass.{u1, u1, u1} F (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.semiring.{u1} F (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, u1} F F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (CommSemiring.toSemiring.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))))))))) (Polynomial.expand.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) q m')) g')) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g) -> (Polynomial.Separable.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)) g') -> (Eq.{1} Nat (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) g) (Polynomial.natDegree.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) g'))
+Case conversion may be inaccurate. Consider using '#align polynomial.contraction_degree_eq_or_insep Polynomial.contraction_degree_eq_or_insepₓ'. -/
 /-- If two expansions (along the positive characteristic) of two separable polynomials `g` and `g'`
 agree, then they have the same degree. -/
 theorem contraction_degree_eq_or_insep [hq : NeZero q] [CharP F q] (g g' : F[X]) (m m' : ℕ)
@@ -133,6 +165,7 @@ theorem contraction_degree_eq_or_insep [hq : NeZero q] [CharP F q] (g g' : F[X])
   · rw [nat_degree_expand, pow_zero, mul_one]
 #align polynomial.contraction_degree_eq_or_insep Polynomial.contraction_degree_eq_or_insep
 
+#print Polynomial.IsSeparableContraction.degree_eq /-
 /-- The separable degree equals the degree of any separable contraction, i.e., it is unique. -/
 theorem IsSeparableContraction.degree_eq [hF : ExpChar F q] (g : F[X])
     (hg : IsSeparableContraction q f g) : g.natDegree = hf.degree :=
@@ -151,6 +184,7 @@ theorem IsSeparableContraction.degree_eq [hF : ExpChar F q] (g : F[X])
     exact hg
     exact (Classical.choose_spec hf).1
 #align polynomial.is_separable_contraction.degree_eq Polynomial.IsSeparableContraction.degree_eq
+-/
 
 end Field
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/d11893b411025250c8e61ff2f12ccbd7ee35ab15

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jakob Scholbach
 
 ! This file was ported from Lean 3 source module field_theory.separable_degree
-! leanprover-community/mathlib commit 92ca63f0fb391a9ca5f22d2409a6080e786d99f7
+! leanprover-community/mathlib commit d11893b411025250c8e61ff2f12ccbd7ee35ab15
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -48,7 +48,7 @@ open Classical Polynomial
 
 section CommSemiring
 
-variable {F : Type} [CommSemiring F] (q : ℕ)
+variable {F : Type _} [CommSemiring F] (q : ℕ)
 
 /-- A separable contraction of a polynomial `f` is a separable polynomial `g` such that
 `g(x^(q^m)) = f(x)` for some `m : ℕ`.-/
@@ -103,7 +103,7 @@ end CommSemiring
 
 section Field
 
-variable {F : Type} [Field F]
+variable {F : Type _} [Field F]
 
 variable (q : ℕ) {f : F[X]} (hf : HasSeparableContraction q f)
 

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

@@ -129,7 +129,7 @@ theorem contraction_degree_eq_or_insep [hq : NeZero q] [CharP F q] (g g' : F[X])
   rw [pow_add, expand_mul, expand_inj (pow_pos (NeZero.pos q) m)] at h_expand
   subst h_expand
   rcases is_unit_or_eq_zero_of_separable_expand q s (NeZero.pos q) hg with (h | rfl)
-  · rw [nat_degree_expand, nat_degree_eq_zero_of_is_unit h, zero_mul]
+  · rw [nat_degree_expand, nat_degree_eq_zero_of_is_unit h, MulZeroClass.zero_mul]
   · rw [nat_degree_expand, pow_zero, mul_one]
 #align polynomial.contraction_degree_eq_or_insep Polynomial.contraction_degree_eq_or_insep
 

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

Splits Algebra.Algebra.Defs off Algebra.Algebra.Basic. Most imports only need the Defs file, which has significantly smaller imports. The remaining Algebra.Algebra.Basic is now a grab-bag of unrelated results, and should probably be split further or rehomed.

This is mostly motivated by the wasted effort during minimization upon encountering Algebra.Algebra.Basic.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

@@ -3,7 +3,7 @@ Copyright (c) 2021 Jakob Scholbach. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jakob Scholbach
 -/
-import Mathlib.Algebra.Algebra.Basic
+import Mathlib.Algebra.Algebra.Defs
 import Mathlib.Algebra.CharP.ExpChar
 import Mathlib.FieldTheory.Separable
 

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

@@ -48,7 +48,7 @@ section CommSemiring
 variable {F : Type*} [CommSemiring F] (q : ℕ)
 
 /-- A separable contraction of a polynomial `f` is a separable polynomial `g` such that
-`g(x^(q^m)) = f(x)` for some `m : ℕ`.-/
+`g(x^(q^m)) = f(x)` for some `m : ℕ`. -/
 def IsSeparableContraction (f : F[X]) (g : F[X]) : Prop :=
   g.Separable ∧ ∃ m : ℕ, expand F (q ^ m) g = f
 #align polynomial.is_separable_contraction Polynomial.IsSeparableContraction

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -104,7 +104,6 @@ end CommSemiring
 section Field
 
 variable {F : Type*} [Field F]
-
 variable (q : ℕ) {f : F[X]} (hf : HasSeparableContraction q f)
 
 /-- Every irreducible polynomial can be contracted to a separable polynomial.

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -40,7 +40,8 @@ noncomputable section
 
 namespace Polynomial
 
-open Classical Polynomial
+open scoped Classical
+open Polynomial
 
 section CommSemiring
 

… move Irreducible.hasSeparableContraction to global namespace

@@ -22,7 +22,7 @@ This file contains basics about the separable degree of a polynomial.
 - `HasSeparableContraction`: the condition of having a separable contraction
 - `HasSeparableContraction.degree`: the separable degree, defined as the degree of some
   separable contraction
-- `Irreducible.HasSeparableContraction`: any irreducible polynomial can be contracted
+- `Irreducible.hasSeparableContraction`: any irreducible polynomial can be contracted
   to a separable polynomial
 - `HasSeparableContraction.dvd_degree'`: the degree of a separable contraction divides the degree,
   in function of the exponential characteristic of the field
@@ -69,6 +69,10 @@ def HasSeparableContraction.degree : ℕ :=
   hf.contraction.natDegree
 #align polynomial.has_separable_contraction.degree Polynomial.HasSeparableContraction.degree
 
+/-- The `HasSeparableContraction.contraction` is indeed a separable contraction. -/
+theorem HasSeparableContraction.isSeparableContraction :
+    IsSeparableContraction q f hf.contraction := Classical.choose_spec hf
+
 /-- The separable degree divides the degree, in function of the exponential characteristic of F. -/
 theorem IsSeparableContraction.dvd_degree' {g} (hf : IsSeparableContraction q f g) :
     ∃ m : ℕ, g.natDegree * q ^ m = f.natDegree := by
@@ -104,13 +108,13 @@ variable (q : ℕ) {f : F[X]} (hf : HasSeparableContraction q f)
 
 /-- Every irreducible polynomial can be contracted to a separable polynomial.
 https://stacks.math.columbia.edu/tag/09H0 -/
-theorem Irreducible.hasSeparableContraction (q : ℕ) [hF : ExpChar F q] (f : F[X])
+theorem _root_.Irreducible.hasSeparableContraction (q : ℕ) [hF : ExpChar F q] {f : F[X]}
     (irred : Irreducible f) : HasSeparableContraction q f := by
   cases hF
   · exact ⟨f, irred.separable, ⟨0, by rw [pow_zero, expand_one]⟩⟩
   · rcases exists_separable_of_irreducible q irred ‹q.Prime›.ne_zero with ⟨n, g, hgs, hge⟩
     exact ⟨g, hgs, n, hge⟩
-#align irreducible.has_separable_contraction Polynomial.Irreducible.hasSeparableContraction
+#align irreducible.has_separable_contraction Irreducible.hasSeparableContraction
 
 /-- If two expansions (along the positive characteristic) of two separable polynomials `g` and `g'`
 agree, then they have the same degree. -/

Main changes:

• rename current Mathlib/FieldTheory/SeparableDegree to Mathlib/RingTheory/Polynomial/SeparableDegree and create new Mathlib/FieldTheory/SeparableDegree

Main definitions

• Emb F E: the type of F-algebra homomorphisms from E to the algebraic closure of E.

• sepDegree F E: the separable degree of an algebraic extension E / F of fields, defined to be the cardinal of F-algebra homomorphisms from E to the algebraic closure of E. (Mathematically, it should be the algebraic closure of F, but in order to make the type compatible with Module.rank F E, we use the algebraic closure of E.) Note that if E / F is not algebraic, then this definition makes no mathematical sense.

• finSepDegree F E: the separable degree of E / F as a natural number, which is zero if sepDegree F E is not finite.

Main results

• embEquivOfEquiv, sepDegree_eq_of_equiv, finSepDegree_eq_of_equiv: a random isomorphism between Emb F E and Emb F E' when E and E' are isomorphic as F-algebras. In particular, they have the same cardinality (so sepDegree and finSepDegree are equal).

• embEquivOfAdjoinSplits', sepDegree_eq_of_adjoin_splits', finSepDegree_eq_of_adjoin_splits': a random isomorphism between Emb F E and E →ₐ[F] K if E = F(S) such that every element s of S is integral (= algebraic) over F and whose minimal polynomial splits in K. In particular, they have the same cardinality.

• embEquivOfIsAlgClosed, sepDegree_eq_of_isAlgClosed, finSepDegree_eq_of_isAlgClosed: a random isomorphism between Emb F E and E →ₐ[F] K when E / F is algebraic and K / F is algebraically closed. In particular, they have the same cardinality.

• embProdEmbOfIsAlgebraic, lift_sepDegree_mul_lift_sepDegree_of_isAlgebraic, sepDegree_mul_sepDegree_of_isAlgebraic, finSepDegree_mul_finSepDegree_of_isAlgebraic: if K / E / F is a field extension tower, such that K / E is algebraic, then there is a non-canonical isomorphism (Emb F E) × (Emb E K) ≃ (Emb F K). In particular, the separable degree satisfies the tower law: [E:F]_s [K:E]_s = [K:F]_s.

@@ -136,12 +136,10 @@ theorem IsSeparableContraction.degree_eq [hF : ExpChar F q] (g : F[X])
     rw [hf.eq_degree, hm]
   · rcases hg with ⟨hg, m, hm⟩
     let g' := Classical.choose hf
-    cases' (Classical.choose_spec hf).2 with m' hm'
+    obtain ⟨hg', m', hm'⟩ := Classical.choose_spec hf
     haveI : Fact q.Prime := ⟨by assumption⟩
-    apply contraction_degree_eq_or_insep q g g' m m'
+    refine contraction_degree_eq_or_insep q g g' m m' ?_ hg hg'
     rw [hm, hm']
-    exact hg
-    exact (Classical.choose_spec hf).1
 #align polynomial.is_separable_contraction.degree_eq Polynomial.IsSeparableContraction.degree_eq
 
 end Field

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -123,7 +123,7 @@ theorem contraction_degree_eq_or_insep [hq : NeZero q] [CharP F q] (g g' : F[X])
   rw [pow_add, expand_mul, expand_inj (pow_pos (NeZero.pos q) m)] at h_expand
   subst h_expand
   rcases isUnit_or_eq_zero_of_separable_expand q s (NeZero.pos q) hg with (h | rfl)
-  · rw [natDegree_expand, natDegree_eq_zero_of_isUnit h, MulZeroClass.zero_mul]
+  · rw [natDegree_expand, natDegree_eq_zero_of_isUnit h, zero_mul]
   · rw [natDegree_expand, pow_zero, mul_one]
 #align polynomial.contraction_degree_eq_or_insep Polynomial.contraction_degree_eq_or_insep
 

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

This has nice performance benefits.

@@ -44,7 +44,7 @@ open Classical Polynomial
 
 section CommSemiring
 
-variable {F : Type _} [CommSemiring F] (q : ℕ)
+variable {F : Type*} [CommSemiring F] (q : ℕ)
 
 /-- A separable contraction of a polynomial `f` is a separable polynomial `g` such that
 `g(x^(q^m)) = f(x)` for some `m : ℕ`.-/
@@ -98,7 +98,7 @@ end CommSemiring
 
 section Field
 
-variable {F : Type _} [Field F]
+variable {F : Type*} [Field F]
 
 variable (q : ℕ) {f : F[X]} (hf : HasSeparableContraction q f)
 

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Jakob Scholbach. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jakob Scholbach
-
-! This file was ported from Lean 3 source module field_theory.separable_degree
-! leanprover-community/mathlib commit d11893b411025250c8e61ff2f12ccbd7ee35ab15
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Algebra.Basic
 import Mathlib.Algebra.CharP.ExpChar
 import Mathlib.FieldTheory.Separable
 
+#align_import field_theory.separable_degree from "leanprover-community/mathlib"@"d11893b411025250c8e61ff2f12ccbd7ee35ab15"
+
 /-!
 
 # Separable degree

These are all doc fixes

@@ -55,7 +55,7 @@ def IsSeparableContraction (f : F[X]) (g : F[X]) : Prop :=
   g.Separable ∧ ∃ m : ℕ, expand F (q ^ m) g = f
 #align polynomial.is_separable_contraction Polynomial.IsSeparableContraction
 
-/-- The condition of having a separable contration. -/
+/-- The condition of having a separable contraction. -/
 def HasSeparableContraction (f : F[X]) : Prop :=
   ∃ g : F[X], IsSeparableContraction q f g
 #align polynomial.has_separable_contraction Polynomial.HasSeparableContraction