number_theory.number_field.class_number

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

d0259b01

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

30faa0c3

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2021 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 -/
-import Mathbin.NumberTheory.ClassNumber.AdmissibleAbs
-import Mathbin.NumberTheory.ClassNumber.Finite
-import Mathbin.NumberTheory.NumberField.Basic
+import NumberTheory.ClassNumber.AdmissibleAbs
+import NumberTheory.ClassNumber.Finite
+import NumberTheory.NumberField.Basic
 
 #align_import number_theory.number_field.class_number from "leanprover-community/mathlib"@"30faa0c3618ce1472bf6305ae0e3fa56affa3f95"

30faa0c3

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
-
-! This file was ported from Lean 3 source module number_theory.number_field.class_number
-! leanprover-community/mathlib commit 30faa0c3618ce1472bf6305ae0e3fa56affa3f95
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.NumberTheory.ClassNumber.AdmissibleAbs
 import Mathbin.NumberTheory.ClassNumber.Finite
 import Mathbin.NumberTheory.NumberField.Basic
 
+#align_import number_theory.number_field.class_number from "leanprover-community/mathlib"@"30faa0c3618ce1472bf6305ae0e3fa56affa3f95"
+
 /-!
 # Class numbers of number fields

30faa0c3

bump to nightly-2023-06-27-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9

b5e0c440

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 
 ! This file was ported from Lean 3 source module number_theory.number_field.class_number
-! leanprover-community/mathlib commit d0259b01c82eed3f50390a60404c63faf9e60b1f
+! leanprover-community/mathlib commit 30faa0c3618ce1472bf6305ae0e3fa56affa3f95
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.NumberTheory.NumberField.Basic
 /-!
 # Class numbers of number fields
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines the class number of a number field as the (finite) cardinality of
 the class group of its ring of integers. It also proves some elementary results
 on the class number.

d0259b01

bump to nightly-2023-06-24-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/93f880918cb51905fd51b76add8273cbc27718ab

fad49451

Diff

@@ -36,17 +36,21 @@ noncomputable instance : Fintype (ClassGroup (ringOfIntegers K)) :=
 
 end RingOfIntegers
 
+#print NumberField.classNumber /-
 /-- The class number of a number field is the (finite) cardinality of the class group. -/
 noncomputable def classNumber : ℕ :=
   Fintype.card (ClassGroup (ringOfIntegers K))
 #align number_field.class_number NumberField.classNumber
+-/
 
 variable {K}
 
+#print NumberField.classNumber_eq_one_iff /-
 /-- The class number of a number field is `1` iff the ring of integers is a PID. -/
 theorem classNumber_eq_one_iff : classNumber K = 1 ↔ IsPrincipalIdealRing (ringOfIntegers K) :=
   card_classGroup_eq_one_iff
 #align number_field.class_number_eq_one_iff NumberField.classNumber_eq_one_iff
+-/
 
 end NumberField
 
@@ -54,6 +58,7 @@ namespace Rat
 
 open NumberField
 
+#print Rat.classNumber_eq /-
 theorem classNumber_eq : NumberField.classNumber ℚ = 1 :=
   classNumber_eq_one_iff.mpr <| by
     convert
@@ -61,6 +66,7 @@ theorem classNumber_eq : NumberField.classNumber ℚ = 1 :=
         (rat.ring_of_integers_equiv.symm : ℤ →+* ring_of_integers ℚ)
         rat.ring_of_integers_equiv.symm.surjective
 #align rat.class_number_eq Rat.classNumber_eq
+-/
 
 end Rat

d0259b01

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -56,7 +56,8 @@ open NumberField
 
 theorem classNumber_eq : NumberField.classNumber ℚ = 1 :=
   classNumber_eq_one_iff.mpr <| by
-    convert IsPrincipalIdealRing.of_surjective
+    convert
+      IsPrincipalIdealRing.of_surjective
         (rat.ring_of_integers_equiv.symm : ℤ →+* ring_of_integers ℚ)
         rat.ring_of_integers_equiv.symm.surjective
 #align rat.class_number_eq Rat.classNumber_eq

d0259b01

bump to nightly-2023-03-17-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

c85864d4

Diff

@@ -56,8 +56,7 @@ open NumberField
 
 theorem classNumber_eq : NumberField.classNumber ℚ = 1 :=
   classNumber_eq_one_iff.mpr <| by
-    convert
-      IsPrincipalIdealRing.of_surjective
+    convert IsPrincipalIdealRing.of_surjective
         (rat.ring_of_integers_equiv.symm : ℤ →+* ring_of_integers ℚ)
         rat.ring_of_integers_equiv.symm.surjective
 #align rat.class_number_eq Rat.classNumber_eq

d0259b01

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

d0259b01

chore: Delete Init.Data.Subtype.Basic (#11887)

The few useful lemmas can go to Data.Subtype.Basic and the other ones can be deleted.

cfc96fe7

Diff

@@ -64,7 +64,7 @@ theorem exists_ideal_in_class_of_norm_le (C : ClassGroup (𝓞 K)):
   let I := (⟨I₀, mem_nonZeroDivisors_iff_ne_zero.mpr this⟩ : (Ideal (𝓞 K))⁰)
   refine ⟨I, ?_, ?_⟩
   · suffices ClassGroup.mk0 I = (ClassGroup.mk0 J)⁻¹ by rw [this, hJ, inv_inv]
-    exact ClassGroup.mk0_eq_mk0_inv_iff.mpr ⟨a, Subtype.ne_of_val_ne h_nz, by rw [mul_comm, hI]⟩
+    exact ClassGroup.mk0_eq_mk0_inv_iff.mpr ⟨a, Subtype.coe_ne_coe.1 h_nz, by rw [mul_comm, hI]⟩
   · rw [← FractionalIdeal.absNorm_span_singleton (𝓞 K), Algebra.linearMap_apply,
       ← FractionalIdeal.coeIdeal_span_singleton, FractionalIdeal.coeIdeal_absNorm, hI, map_mul,
       Nat.cast_mul, Rat.cast_mul, show Ideal.absNorm I₀ = Ideal.absNorm (I : Ideal (𝓞 K)) by rfl,

d0259b01

chore: Rename cat_coe_nat/cast_coe_int to cast_natCast/cast_intCast (#11552)

Reduce the diff of #11499

026dd701

Diff

@@ -68,8 +68,8 @@ theorem exists_ideal_in_class_of_norm_le (C : ClassGroup (𝓞 K)):
   · rw [← FractionalIdeal.absNorm_span_singleton (𝓞 K), Algebra.linearMap_apply,
       ← FractionalIdeal.coeIdeal_span_singleton, FractionalIdeal.coeIdeal_absNorm, hI, map_mul,
       Nat.cast_mul, Rat.cast_mul, show Ideal.absNorm I₀ = Ideal.absNorm (I : Ideal (𝓞 K)) by rfl,
-      Rat.cast_coe_nat, Rat.cast_coe_nat, FractionalIdeal.coe_mk0,
-      FractionalIdeal.coeIdeal_absNorm, Rat.cast_coe_nat, mul_div_assoc, mul_assoc, mul_assoc]
+      Rat.cast_natCast, Rat.cast_natCast, FractionalIdeal.coe_mk0,
+      FractionalIdeal.coeIdeal_absNorm, Rat.cast_natCast, mul_div_assoc, mul_assoc, mul_assoc]
       at h_nm
     refine le_of_mul_le_mul_of_pos_left h_nm ?_
     exact Nat.cast_pos.mpr <| Nat.pos_of_ne_zero <| Ideal.absNorm_ne_zero_of_nonZeroDivisors J

d0259b01

feat: Add exists_ideal_in_class_of_norm_le (#9084)

Prove that each class of the classgroup of a number field contains an integral ideal of small norm.

3e8b888d

Diff

@@ -5,7 +5,7 @@ Authors: Anne Baanen
 -/
 import Mathlib.NumberTheory.ClassNumber.AdmissibleAbs
 import Mathlib.NumberTheory.ClassNumber.Finite
-import Mathlib.NumberTheory.NumberField.Basic
+import Mathlib.NumberTheory.NumberField.Discriminant
 
 #align_import number_theory.number_field.class_number from "leanprover-community/mathlib"@"d0259b01c82eed3f50390a60404c63faf9e60b1f"
 
@@ -45,6 +45,52 @@ theorem classNumber_eq_one_iff : classNumber K = 1 ↔ IsPrincipalIdealRing (rin
   card_classGroup_eq_one_iff
 #align number_field.class_number_eq_one_iff NumberField.classNumber_eq_one_iff
 
+open FiniteDimensional NumberField.InfinitePlace
+
+open scoped nonZeroDivisors Real
+
+theorem exists_ideal_in_class_of_norm_le (C : ClassGroup (𝓞 K)):
+    ∃ I : (Ideal (𝓞 K))⁰, ClassGroup.mk0 I = C ∧
+      Ideal.absNorm (I : Ideal (𝓞 K)) ≤ (4 / π) ^ NrComplexPlaces K *
+        ((finrank ℚ K).factorial / (finrank ℚ K) ^ (finrank ℚ K) * Real.sqrt |discr K|) := by
+  obtain ⟨J, hJ⟩ := ClassGroup.mk0_surjective C⁻¹
+  obtain ⟨_, ⟨a, ha, rfl⟩, h_nz, h_nm⟩ :=
+    exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr K (FractionalIdeal.mk0 K J)
+  obtain ⟨I₀, hI⟩ := Ideal.dvd_iff_le.mpr ((Ideal.span_singleton_le_iff_mem J).mpr (by convert ha))
+  have : I₀ ≠ 0 := by
+    contrapose! h_nz
+    rw [h_nz, mul_zero, show 0 = (⊥ : Ideal (𝓞 K)) by rfl, Ideal.span_singleton_eq_bot] at hI
+    rw [Algebra.linearMap_apply, hI, map_zero]
+  let I := (⟨I₀, mem_nonZeroDivisors_iff_ne_zero.mpr this⟩ : (Ideal (𝓞 K))⁰)
+  refine ⟨I, ?_, ?_⟩
+  · suffices ClassGroup.mk0 I = (ClassGroup.mk0 J)⁻¹ by rw [this, hJ, inv_inv]
+    exact ClassGroup.mk0_eq_mk0_inv_iff.mpr ⟨a, Subtype.ne_of_val_ne h_nz, by rw [mul_comm, hI]⟩
+  · rw [← FractionalIdeal.absNorm_span_singleton (𝓞 K), Algebra.linearMap_apply,
+      ← FractionalIdeal.coeIdeal_span_singleton, FractionalIdeal.coeIdeal_absNorm, hI, map_mul,
+      Nat.cast_mul, Rat.cast_mul, show Ideal.absNorm I₀ = Ideal.absNorm (I : Ideal (𝓞 K)) by rfl,
+      Rat.cast_coe_nat, Rat.cast_coe_nat, FractionalIdeal.coe_mk0,
+      FractionalIdeal.coeIdeal_absNorm, Rat.cast_coe_nat, mul_div_assoc, mul_assoc, mul_assoc]
+      at h_nm
+    refine le_of_mul_le_mul_of_pos_left h_nm ?_
+    exact Nat.cast_pos.mpr <| Nat.pos_of_ne_zero <| Ideal.absNorm_ne_zero_of_nonZeroDivisors J
+
+theorem _root_.RingOfIntegers.isPrincipalIdealRing_of_abs_discr_lt
+    (h : |discr K| < (2 * (π / 4) ^ NrComplexPlaces K *
+      ((finrank ℚ K) ^ (finrank ℚ K) / (finrank ℚ K).factorial)) ^ 2) :
+    IsPrincipalIdealRing (ringOfIntegers K) := by
+  have : 0 < finrank ℚ K := finrank_pos -- Lean needs to know that for positivity to succeed
+  rw [← Real.sqrt_lt (by positivity) (by positivity), mul_assoc, ← inv_mul_lt_iff' (by positivity),
+    mul_inv, ← inv_pow, inv_div, inv_div, mul_assoc, Int.cast_abs] at h
+  rw [← classNumber_eq_one_iff, classNumber, Fintype.card_eq_one_iff]
+  refine ⟨1, fun C ↦ ?_⟩
+  obtain ⟨I, rfl, hI⟩ := exists_ideal_in_class_of_norm_le C
+  have : Ideal.absNorm I.1 = 1 := by
+    refine le_antisymm (Nat.lt_succ.mp ?_) (Nat.one_le_iff_ne_zero.mpr
+      (Ideal.absNorm_ne_zero_of_nonZeroDivisors I))
+    exact Nat.cast_lt.mp <| lt_of_le_of_lt hI h
+  rw [ClassGroup.mk0_eq_one_iff, Ideal.absNorm_eq_one_iff.mp this]
+  exact top_isPrincipal
+
 end NumberField
 
 namespace Rat

d0259b01

doc: add an algebraic number theory section to Mathlib overview (#7429)

5eb77486

Diff

@@ -28,7 +28,7 @@ variable (K : Type*) [Field K] [NumberField K]
 
 namespace RingOfIntegers
 
-noncomputable instance : Fintype (ClassGroup (ringOfIntegers K)) :=
+noncomputable instance instFintypeClassGroup : Fintype (ClassGroup (ringOfIntegers K)) :=
   ClassGroup.fintypeOfAdmissibleOfFinite ℚ K AbsoluteValue.absIsAdmissible
 
 end RingOfIntegers

d0259b01

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -24,7 +24,7 @@ cardinality of the class group of its ring of integers
 
 namespace NumberField
 
-variable (K : Type _) [Field K] [NumberField K]
+variable (K : Type*) [Field K] [NumberField K]
 
 namespace RingOfIntegers

d0259b01

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
-
-! This file was ported from Lean 3 source module number_theory.number_field.class_number
-! leanprover-community/mathlib commit d0259b01c82eed3f50390a60404c63faf9e60b1f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.NumberTheory.ClassNumber.AdmissibleAbs
 import Mathlib.NumberTheory.ClassNumber.Finite
 import Mathlib.NumberTheory.NumberField.Basic
 
+#align_import number_theory.number_field.class_number from "leanprover-community/mathlib"@"d0259b01c82eed3f50390a60404c63faf9e60b1f"
+
 /-!
 # Class numbers of number fields

d0259b01

feat: port NumberTheory.NumberField.ClassNumber (#5456)

fab65d80

`number_theory.number_field.class_number` ⟷ `Mathlib.NumberTheory.NumberField.ClassNumber`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 938

number_theory.number_field.class_number ⟷ Mathlib.NumberTheory.NumberField.ClassNumber

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 938

`number_theory.number_field.class_number` ⟷ `Mathlib.NumberTheory.NumberField.ClassNumber`