number_theory.bernoulli_polynomials | Mathlib porting status

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

ca3d21f7

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

fd4551cf

bump to nightly-2024-04-07-08

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

b03b8656

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Ashvni Narayanan. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Ashvni Narayanan, David Loeffler
 -/
-import Data.Polynomial.AlgebraMap
-import Data.Polynomial.Derivative
+import Algebra.Polynomial.AlgebraMap
+import Algebra.Polynomial.Derivative
 import Data.Nat.Choose.Cast
 import NumberTheory.Bernoulli

fd4551cf

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -184,7 +184,7 @@ theorem bernoulli_eq_sub_sum (n : ℕ) :
     (n.succ : ℚ) • bernoulli n =
       monomial n (n.succ : ℚ) - ∑ k in Finset.range n, ((n + 1).choose k : ℚ) • bernoulli k :=
   by
-  rw [Nat.cast_succ, ← sum_bernoulli n, sum_range_succ, add_sub_cancel', choose_succ_self_right,
+  rw [Nat.cast_succ, ← sum_bernoulli n, sum_range_succ, add_sub_cancel_left, choose_succ_self_right,
     Nat.cast_succ]
 #align polynomial.bernoulli_eq_sub_sum Polynomial.bernoulli_eq_sub_sum
 -/
@@ -194,7 +194,7 @@ theorem bernoulli_eq_sub_sum (n : ℕ) :
 theorem sum_range_pow_eq_bernoulli_sub (n p : ℕ) :
     (p + 1 : ℚ) * ∑ k in range n, (k : ℚ) ^ p = (bernoulli p.succ).eval n - bernoulli p.succ :=
   by
-  rw [sum_range_pow, bernoulli_def, eval_finset_sum, ← sum_div, mul_div_cancel' _ _]
+  rw [sum_range_pow, bernoulli_def, eval_finset_sum, ← sum_div, mul_div_cancel₀ _ _]
   · simp_rw [eval_monomial]
     symm
     rw [← sum_flip _, sum_range_succ]

fd4551cf

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -68,7 +68,7 @@ theorem bernoulli_def (n : ℕ) :
   rw [← sum_range_reflect, add_succ_sub_one, add_zero, bernoulli]
   apply sum_congr rfl
   rintro x hx
-  rw [mem_range_succ_iff] at hx ; rw [choose_symm hx, tsub_tsub_cancel_of_le hx]
+  rw [mem_range_succ_iff] at hx; rw [choose_symm hx, tsub_tsub_cancel_of_le hx]
 #align polynomial.bernoulli_def Polynomial.bernoulli_def
 -/
 
@@ -165,7 +165,7 @@ theorem sum_bernoulli (n : ℕ) :
     LinearMap.map_add, range_one]
   apply sum_eq_zero fun x hx => _
   have f : ∀ x ∈ range n, ¬n + 1 - x = 1 := by
-    rintro x H; rw [mem_range] at H 
+    rintro x H; rw [mem_range] at H
     rw [eq_comm]
     exact ne_of_lt (Nat.lt_of_lt_of_le one_lt_two (le_tsub_of_add_le_left (succ_le_succ H)))
   rw [sum_bernoulli]

fd4551cf

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2021 Ashvni Narayanan. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Ashvni Narayanan, David Loeffler
 -/
-import Mathbin.Data.Polynomial.AlgebraMap
-import Mathbin.Data.Polynomial.Derivative
-import Mathbin.Data.Nat.Choose.Cast
-import Mathbin.NumberTheory.Bernoulli
+import Data.Polynomial.AlgebraMap
+import Data.Polynomial.Derivative
+import Data.Nat.Choose.Cast
+import NumberTheory.Bernoulli
 
 #align_import number_theory.bernoulli_polynomials from "leanprover-community/mathlib"@"fd4551cfe4b7484b81c2c9ba3405edae27659676"

fd4551cf

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Ashvni Narayanan. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Ashvni Narayanan, David Loeffler
-
-! This file was ported from Lean 3 source module number_theory.bernoulli_polynomials
-! leanprover-community/mathlib commit fd4551cfe4b7484b81c2c9ba3405edae27659676
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Polynomial.AlgebraMap
 import Mathbin.Data.Polynomial.Derivative
 import Mathbin.Data.Nat.Choose.Cast
 import Mathbin.NumberTheory.Bernoulli
 
+#align_import number_theory.bernoulli_polynomials from "leanprover-community/mathlib"@"fd4551cfe4b7484b81c2c9ba3405edae27659676"
+
 /-!
 # Bernoulli polynomials

fd4551cf

bump to nightly-2023-06-21-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/f2ad3645af9effcdb587637dc28a6074edc813f9

78c41114

Diff

@@ -133,12 +133,14 @@ theorem derivative_bernoulli_add_one (k : ℕ) :
 #align polynomial.derivative_bernoulli_add_one Polynomial.derivative_bernoulli_add_one
 -/
 
+#print Polynomial.derivative_bernoulli /-
 theorem derivative_bernoulli (k : ℕ) : (bernoulli k).derivative = k * bernoulli (k - 1) :=
   by
   cases k
   · rw [Nat.cast_zero, MulZeroClass.zero_mul, bernoulli_zero, derivative_one]
   · exact_mod_cast derivative_bernoulli_add_one k
 #align polynomial.derivative_bernoulli Polynomial.derivative_bernoulli
+-/
 
 #print Polynomial.sum_bernoulli /-
 @[simp]

fd4551cf

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -64,6 +64,7 @@ def bernoulli (n : ℕ) : ℚ[X] :=
 #align polynomial.bernoulli Polynomial.bernoulli
 -/
 
+#print Polynomial.bernoulli_def /-
 theorem bernoulli_def (n : ℕ) :
     bernoulli n = ∑ i in range (n + 1), Polynomial.monomial i (bernoulli (n - i) * choose n i) :=
   by
@@ -72,6 +73,7 @@ theorem bernoulli_def (n : ℕ) :
   rintro x hx
   rw [mem_range_succ_iff] at hx ; rw [choose_symm hx, tsub_tsub_cancel_of_le hx]
 #align polynomial.bernoulli_def Polynomial.bernoulli_def
+-/
 
 /-
 ### examples
@@ -114,6 +116,7 @@ theorem bernoulli_eval_one (n : ℕ) : (bernoulli n).eval 1 = bernoulli' n :=
 
 end Examples
 
+#print Polynomial.derivative_bernoulli_add_one /-
 theorem derivative_bernoulli_add_one (k : ℕ) :
     (bernoulli (k + 1)).derivative = (k + 1) * bernoulli k :=
   by
@@ -128,6 +131,7 @@ theorem derivative_bernoulli_add_one (k : ℕ) :
   congr 3
   rw [(choose_mul_succ_eq k m).symm, mul_comm]
 #align polynomial.derivative_bernoulli_add_one Polynomial.derivative_bernoulli_add_one
+-/
 
 theorem derivative_bernoulli (k : ℕ) : (bernoulli k).derivative = k * bernoulli (k - 1) :=
   by
@@ -175,6 +179,7 @@ theorem sum_bernoulli (n : ℕ) :
 #align polynomial.sum_bernoulli Polynomial.sum_bernoulli
 -/
 
+#print Polynomial.bernoulli_eq_sub_sum /-
 /-- Another version of `polynomial.sum_bernoulli`. -/
 theorem bernoulli_eq_sub_sum (n : ℕ) :
     (n.succ : ℚ) • bernoulli n =
@@ -183,7 +188,9 @@ theorem bernoulli_eq_sub_sum (n : ℕ) :
   rw [Nat.cast_succ, ← sum_bernoulli n, sum_range_succ, add_sub_cancel', choose_succ_self_right,
     Nat.cast_succ]
 #align polynomial.bernoulli_eq_sub_sum Polynomial.bernoulli_eq_sub_sum
+-/
 
+#print Polynomial.sum_range_pow_eq_bernoulli_sub /-
 /-- Another version of `bernoulli.sum_range_pow`. -/
 theorem sum_range_pow_eq_bernoulli_sub (n p : ℕ) :
     (p + 1 : ℚ) * ∑ k in range n, (k : ℚ) ^ p = (bernoulli p.succ).eval n - bernoulli p.succ :=
@@ -200,13 +207,17 @@ theorem sum_range_pow_eq_bernoulli_sub (n p : ℕ) :
     · rw [← choose_symm (mem_range_le hx)]
   · norm_cast; apply succ_ne_zero _
 #align polynomial.sum_range_pow_eq_bernoulli_sub Polynomial.sum_range_pow_eq_bernoulli_sub
+-/
 
+#print Polynomial.bernoulli_succ_eval /-
 /-- Rearrangement of `polynomial.sum_range_pow_eq_bernoulli_sub`. -/
 theorem bernoulli_succ_eval (n p : ℕ) :
     (bernoulli p.succ).eval n = bernoulli p.succ + (p + 1 : ℚ) * ∑ k in range n, (k : ℚ) ^ p := by
   apply eq_add_of_sub_eq'; rw [sum_range_pow_eq_bernoulli_sub]
 #align polynomial.bernoulli_succ_eval Polynomial.bernoulli_succ_eval
+-/
 
+#print Polynomial.bernoulli_eval_one_add /-
 theorem bernoulli_eval_one_add (n : ℕ) (x : ℚ) :
     (bernoulli n).eval (1 + x) = (bernoulli n).eval x + n * x ^ (n - 1) :=
   by
@@ -232,11 +243,13 @@ theorem bernoulli_eval_one_add (n : ℕ) (x : ℚ) :
   rw [Nat.cast_succ, ← smul_eq_mul, ← sum_range_succ _ d, eval_monomial_one_add_sub]
   simp_rw [smul_eq_mul]
 #align polynomial.bernoulli_eval_one_add Polynomial.bernoulli_eval_one_add
+-/
 
 open PowerSeries
 
 variable {A : Type _} [CommRing A] [Algebra ℚ A]
 
+#print Polynomial.bernoulli_generating_function /-
 -- TODO: define exponential generating functions, and use them here
 -- This name should probably be updated afterwards
 /-- The theorem that $(e^X - 1) * ∑ Bₙ(t)* X^n/n! = Xe^{tX}$ -/
@@ -283,6 +296,7 @@ theorem bernoulli_generating_function (t : A) :
   apply congr_arg
   rw [mul_assoc, div_eq_mul_inv, ← mul_inv]
 #align polynomial.bernoulli_generating_function Polynomial.bernoulli_generating_function
+-/
 
 end Polynomial

fd4551cf

bump to nightly-2023-06-11-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/c471da714c044131b90c133701e51b877c246677

6960a941

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Ashvni Narayanan, David Loeffler
 
 ! This file was ported from Lean 3 source module number_theory.bernoulli_polynomials
-! leanprover-community/mathlib commit ca3d21f7f4fd613c2a3c54ac7871163e1e5ecb3a
+! leanprover-community/mathlib commit fd4551cfe4b7484b81c2c9ba3405edae27659676
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.NumberTheory.Bernoulli
 /-!
 # Bernoulli polynomials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The [Bernoulli polynomials](https://en.wikipedia.org/wiki/Bernoulli_polynomials)
 are an important tool obtained from Bernoulli numbers.

ca3d21f7

bump to nightly-2023-06-10-07

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

3fdc57bc

Diff

@@ -86,7 +86,7 @@ theorem bernoulli_zero : bernoulli 0 = 1 := by simp [bernoulli]
 theorem bernoulli_eval_zero (n : ℕ) : (bernoulli n).eval 0 = bernoulli n :=
   by
   rw [bernoulli, eval_finset_sum, sum_range_succ]
-  have : (∑ x : ℕ in range n, _root_.bernoulli x * n.choose x * 0 ^ (n - x)) = 0 :=
+  have : ∑ x : ℕ in range n, _root_.bernoulli x * n.choose x * 0 ^ (n - x) = 0 :=
     by
     apply sum_eq_zero fun x hx => _
     have h : 0 < n - x := tsub_pos_of_lt (mem_range.1 hx)
@@ -136,7 +136,7 @@ theorem derivative_bernoulli (k : ℕ) : (bernoulli k).derivative = k * bernoull
 #print Polynomial.sum_bernoulli /-
 @[simp]
 theorem sum_bernoulli (n : ℕ) :
-    (∑ k in range (n + 1), ((n + 1).choose k : ℚ) • bernoulli k) = monomial n (n + 1 : ℚ) :=
+    ∑ k in range (n + 1), ((n + 1).choose k : ℚ) • bernoulli k = monomial n (n + 1 : ℚ) :=
   by
   simp_rw [bernoulli_def, Finset.smul_sum, Finset.range_eq_Ico, ← Finset.sum_Ico_Ico_comm,
     Finset.sum_Ico_eq_sum_range]
@@ -183,7 +183,7 @@ theorem bernoulli_eq_sub_sum (n : ℕ) :
 
 /-- Another version of `bernoulli.sum_range_pow`. -/
 theorem sum_range_pow_eq_bernoulli_sub (n p : ℕ) :
-    ((p + 1 : ℚ) * ∑ k in range n, (k : ℚ) ^ p) = (bernoulli p.succ).eval n - bernoulli p.succ :=
+    (p + 1 : ℚ) * ∑ k in range n, (k : ℚ) ^ p = (bernoulli p.succ).eval n - bernoulli p.succ :=
   by
   rw [sum_range_pow, bernoulli_def, eval_finset_sum, ← sum_div, mul_div_cancel' _ _]
   · simp_rw [eval_monomial]

ca3d21f7

bump to nightly-2023-06-09-23

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

a380922b

Diff

@@ -54,10 +54,12 @@ open Nat Finset
 
 namespace Polynomial
 
+#print Polynomial.bernoulli /-
 /-- The Bernoulli polynomials are defined in terms of the negative Bernoulli numbers. -/
 def bernoulli (n : ℕ) : ℚ[X] :=
   ∑ i in range (n + 1), Polynomial.monomial (n - i) (bernoulli i * choose n i)
 #align polynomial.bernoulli Polynomial.bernoulli
+-/
 
 theorem bernoulli_def (n : ℕ) :
     bernoulli n = ∑ i in range (n + 1), Polynomial.monomial i (bernoulli (n - i) * choose n i) :=
@@ -73,10 +75,13 @@ theorem bernoulli_def (n : ℕ) :
 -/
 section Examples
 
+#print Polynomial.bernoulli_zero /-
 @[simp]
 theorem bernoulli_zero : bernoulli 0 = 1 := by simp [bernoulli]
 #align polynomial.bernoulli_zero Polynomial.bernoulli_zero
+-/
 
+#print Polynomial.bernoulli_eval_zero /-
 @[simp]
 theorem bernoulli_eval_zero (n : ℕ) : (bernoulli n).eval 0 = bernoulli n :=
   by
@@ -88,7 +93,9 @@ theorem bernoulli_eval_zero (n : ℕ) : (bernoulli n).eval 0 = bernoulli n :=
     simp [h]
   simp [this]
 #align polynomial.bernoulli_eval_zero Polynomial.bernoulli_eval_zero
+-/
 
+#print Polynomial.bernoulli_eval_one /-
 @[simp]
 theorem bernoulli_eval_one (n : ℕ) : (bernoulli n).eval 1 = bernoulli' n :=
   by
@@ -100,6 +107,7 @@ theorem bernoulli_eval_one (n : ℕ) : (bernoulli n).eval 1 = bernoulli' n :=
   · simp [h]
     exact bernoulli_eq_bernoulli'_of_ne_one h
 #align polynomial.bernoulli_eval_one Polynomial.bernoulli_eval_one
+-/
 
 end Examples
 
@@ -125,6 +133,7 @@ theorem derivative_bernoulli (k : ℕ) : (bernoulli k).derivative = k * bernoull
   · exact_mod_cast derivative_bernoulli_add_one k
 #align polynomial.derivative_bernoulli Polynomial.derivative_bernoulli
 
+#print Polynomial.sum_bernoulli /-
 @[simp]
 theorem sum_bernoulli (n : ℕ) :
     (∑ k in range (n + 1), ((n + 1).choose k : ℚ) • bernoulli k) = monomial n (n + 1 : ℚ) :=
@@ -161,6 +170,7 @@ theorem sum_bernoulli (n : ℕ) :
     exact (f x hx) h₁
   rw [g, zero_smul]
 #align polynomial.sum_bernoulli Polynomial.sum_bernoulli
+-/
 
 /-- Another version of `polynomial.sum_bernoulli`. -/
 theorem bernoulli_eq_sub_sum (n : ℕ) :

ca3d21f7

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -65,7 +65,7 @@ theorem bernoulli_def (n : ℕ) :
   rw [← sum_range_reflect, add_succ_sub_one, add_zero, bernoulli]
   apply sum_congr rfl
   rintro x hx
-  rw [mem_range_succ_iff] at hx; rw [choose_symm hx, tsub_tsub_cancel_of_le hx]
+  rw [mem_range_succ_iff] at hx ; rw [choose_symm hx, tsub_tsub_cancel_of_le hx]
 #align polynomial.bernoulli_def Polynomial.bernoulli_def
 
 /-
@@ -150,7 +150,7 @@ theorem sum_bernoulli (n : ℕ) :
     LinearMap.map_add, range_one]
   apply sum_eq_zero fun x hx => _
   have f : ∀ x ∈ range n, ¬n + 1 - x = 1 := by
-    rintro x H; rw [mem_range] at H
+    rintro x H; rw [mem_range] at H 
     rw [eq_comm]
     exact ne_of_lt (Nat.lt_of_lt_of_le one_lt_two (le_tsub_of_add_le_left (succ_le_succ H)))
   rw [sum_bernoulli]

ca3d21f7

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -46,9 +46,9 @@ Bernoulli polynomials are defined using `bernoulli`, the Bernoulli numbers.
 
 noncomputable section
 
-open BigOperators
+open scoped BigOperators
 
-open Nat Polynomial
+open scoped Nat Polynomial
 
 open Nat Finset

ca3d21f7

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -150,8 +150,7 @@ theorem sum_bernoulli (n : ℕ) :
     LinearMap.map_add, range_one]
   apply sum_eq_zero fun x hx => _
   have f : ∀ x ∈ range n, ¬n + 1 - x = 1 := by
-    rintro x H
-    rw [mem_range] at H
+    rintro x H; rw [mem_range] at H
     rw [eq_comm]
     exact ne_of_lt (Nat.lt_of_lt_of_le one_lt_two (le_tsub_of_add_le_left (succ_le_succ H)))
   rw [sum_bernoulli]
@@ -186,25 +185,20 @@ theorem sum_range_pow_eq_bernoulli_sub (n p : ℕ) :
     apply congr_arg₂ _ (congr_arg₂ _ _ _) rfl
     · rw [Nat.sub_sub_self (mem_range_le hx)]
     · rw [← choose_symm (mem_range_le hx)]
-  · norm_cast
-    apply succ_ne_zero _
+  · norm_cast; apply succ_ne_zero _
 #align polynomial.sum_range_pow_eq_bernoulli_sub Polynomial.sum_range_pow_eq_bernoulli_sub
 
 /-- Rearrangement of `polynomial.sum_range_pow_eq_bernoulli_sub`. -/
 theorem bernoulli_succ_eval (n p : ℕ) :
-    (bernoulli p.succ).eval n = bernoulli p.succ + (p + 1 : ℚ) * ∑ k in range n, (k : ℚ) ^ p :=
-  by
-  apply eq_add_of_sub_eq'
-  rw [sum_range_pow_eq_bernoulli_sub]
+    (bernoulli p.succ).eval n = bernoulli p.succ + (p + 1 : ℚ) * ∑ k in range n, (k : ℚ) ^ p := by
+  apply eq_add_of_sub_eq'; rw [sum_range_pow_eq_bernoulli_sub]
 #align polynomial.bernoulli_succ_eval Polynomial.bernoulli_succ_eval
 
 theorem bernoulli_eval_one_add (n : ℕ) (x : ℚ) :
     (bernoulli n).eval (1 + x) = (bernoulli n).eval x + n * x ^ (n - 1) :=
   by
   apply Nat.strong_induction_on n fun d hd => _
-  have nz : ((d.succ : ℕ) : ℚ) ≠ 0 := by
-    norm_cast
-    exact d.succ_ne_zero
+  have nz : ((d.succ : ℕ) : ℚ) ≠ 0 := by norm_cast; exact d.succ_ne_zero
   apply (mul_right_inj' nz).1
   rw [← smul_eq_mul, ← eval_smul, bernoulli_eq_sub_sum, mul_add, ← smul_eq_mul, ← eval_smul,
     bernoulli_eq_sub_sum, eval_sub, eval_finset_sum]

ca3d21f7

bump to nightly-2023-05-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

ed98987c

Diff

@@ -235,7 +235,7 @@ variable {A : Type _} [CommRing A] [Algebra ℚ A]
 /-- The theorem that $(e^X - 1) * ∑ Bₙ(t)* X^n/n! = Xe^{tX}$ -/
 theorem bernoulli_generating_function (t : A) :
     (mk fun n => aeval t ((1 / n ! : ℚ) • bernoulli n)) * (exp A - 1) =
-      PowerSeries.x * rescale t (exp A) :=
+      PowerSeries.X * rescale t (exp A) :=
   by
   -- check equality of power series by checking coefficients of X^n
   ext n

ca3d21f7

bump to nightly-2023-03-13-10

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

e6823f5e

Diff

@@ -269,8 +269,8 @@ theorem bernoulli_generating_function (t : A) :
   simp only [Nat.cast_choose ℚ (mem_range_le hi), coeff_mk, if_neg (mem_range_sub_ne_zero hi),
     one_div, AlgHom.map_smul, PowerSeries.coeff_one, coeff_exp, sub_zero, LinearMap.map_sub,
     Algebra.smul_mul_assoc, Algebra.smul_def, mul_right_comm _ ((aeval t) _), ← mul_assoc, ←
-    RingHom.map_mul, succ_eq_add_one, ← Polynomial.c_eq_algebraMap, Polynomial.aeval_mul,
-    Polynomial.aeval_c]
+    RingHom.map_mul, succ_eq_add_one, ← Polynomial.C_eq_algebraMap, Polynomial.aeval_mul,
+    Polynomial.aeval_C]
   -- finally cancel the Bernoulli polynomial and the algebra_map
   congr
   apply congr_arg

ca3d21f7

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -108,8 +108,8 @@ theorem derivative_bernoulli_add_one (k : ℕ) :
   by
   simp_rw [bernoulli, derivative_sum, derivative_monomial, Nat.sub_sub, Nat.add_sub_add_right]
   -- LHS sum has an extra term, but the coefficient is zero:
-  rw [range_add_one, sum_insert not_mem_range_self, tsub_self, cast_zero, mul_zero, map_zero,
-    zero_add, mul_sum]
+  rw [range_add_one, sum_insert not_mem_range_self, tsub_self, cast_zero, MulZeroClass.mul_zero,
+    map_zero, zero_add, mul_sum]
   -- the rest of the sum is termwise equal:
   refine' sum_congr (by rfl) fun m hm => _
   conv_rhs => rw [← Nat.cast_one, ← Nat.cast_add, ← C_eq_nat_cast, C_mul_monomial, mul_comm]
@@ -121,7 +121,7 @@ theorem derivative_bernoulli_add_one (k : ℕ) :
 theorem derivative_bernoulli (k : ℕ) : (bernoulli k).derivative = k * bernoulli (k - 1) :=
   by
   cases k
-  · rw [Nat.cast_zero, zero_mul, bernoulli_zero, derivative_one]
+  · rw [Nat.cast_zero, MulZeroClass.zero_mul, bernoulli_zero, derivative_one]
   · exact_mod_cast derivative_bernoulli_add_one k
 #align polynomial.derivative_bernoulli Polynomial.derivative_bernoulli
 
@@ -248,7 +248,7 @@ theorem bernoulli_generating_function (t : A) :
     nat.sum_antidiagonal_eq_sum_range_succ_mk, sum_range_succ]
   -- last term is zero so kill with `add_zero`
   simp only [RingHom.map_sub, tsub_self, constant_coeff_one, constant_coeff_exp,
-    coeff_zero_eq_constant_coeff, mul_zero, sub_self, add_zero]
+    coeff_zero_eq_constant_coeff, MulZeroClass.mul_zero, sub_self, add_zero]
   -- Let's multiply both sides by (n+1)! (OK because it's a unit)
   have hnp1 : IsUnit ((n + 1)! : ℚ) := IsUnit.mk0 _ (by exact_mod_cast factorial_ne_zero (n + 1))
   rw [← (hnp1.map (algebraMap ℚ A)).mul_right_inj]

ca3d21f7

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

ca3d21f7

chore: Rename nat_cast/int_cast/rat_cast to natCast/intCast/ratCast (#11486)

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

145460b9

Diff

@@ -104,7 +104,7 @@ theorem derivative_bernoulli_add_one (k : ℕ) :
     map_zero, zero_add, mul_sum]
   -- the rest of the sum is termwise equal:
   refine' sum_congr (by rfl) fun m _ => _
-  conv_rhs => rw [← Nat.cast_one, ← Nat.cast_add, ← C_eq_nat_cast, C_mul_monomial, mul_comm]
+  conv_rhs => rw [← Nat.cast_one, ← Nat.cast_add, ← C_eq_natCast, C_mul_monomial, mul_comm]
   rw [mul_assoc, mul_assoc, ← Nat.cast_mul, ← Nat.cast_mul]
   congr 3
   rw [(choose_mul_succ_eq k m).symm]

ca3d21f7

chore: tidy various files (#12121)

8fa5a3ae

Diff

@@ -61,7 +61,8 @@ theorem bernoulli_def (n : ℕ) : bernoulli n =
   rw [← sum_range_reflect, add_succ_sub_one, add_zero, bernoulli]
   apply sum_congr rfl
   rintro x hx
-  rw [mem_range_succ_iff] at hx; rw [choose_symm hx, tsub_tsub_cancel_of_le hx]
+  rw [mem_range_succ_iff] at hx
+  rw [choose_symm hx, tsub_tsub_cancel_of_le hx]
 #align polynomial.bernoulli_def Polynomial.bernoulli_def
 
 /-
@@ -76,11 +77,10 @@ theorem bernoulli_zero : bernoulli 0 = 1 := by simp [bernoulli]
 @[simp]
 theorem bernoulli_eval_zero (n : ℕ) : (bernoulli n).eval 0 = _root_.bernoulli n := by
   rw [bernoulli, eval_finset_sum, sum_range_succ]
-  have : (∑ x : ℕ in range n, _root_.bernoulli x * n.choose x * 0 ^ (n - x)) = 0 := by
+  have : ∑ x : ℕ in range n, _root_.bernoulli x * n.choose x * 0 ^ (n - x) = 0 := by
     apply sum_eq_zero fun x hx => _
     intros x hx
-    have h : x < n := mem_range.1 hx
-    simp [tsub_eq_zero_iff_le, h]
+    simp [tsub_eq_zero_iff_le, mem_range.1 hx]
   simp [this]
 #align polynomial.bernoulli_eval_zero Polynomial.bernoulli_eval_zero
 
@@ -91,8 +91,7 @@ theorem bernoulli_eval_one (n : ℕ) : (bernoulli n).eval 1 = bernoulli' n := by
     (_root_.bernoulli _).mul_comm, sum_bernoulli, one_pow, mul_one, eval_C, eval_monomial, one_mul]
   by_cases h : n = 1
   · norm_num [h]
-  · simp [h]
-    exact bernoulli_eq_bernoulli'_of_ne_one h
+  · simp [h, bernoulli_eq_bernoulli'_of_ne_one h]
 #align polynomial.bernoulli_eval_one Polynomial.bernoulli_eval_one
 
 end Examples

ca3d21f7

chore: superfluous parentheses part 2 (#12131)

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

d48d30ac

Diff

@@ -79,7 +79,7 @@ theorem bernoulli_eval_zero (n : ℕ) : (bernoulli n).eval 0 = _root_.bernoulli
   have : (∑ x : ℕ in range n, _root_.bernoulli x * n.choose x * 0 ^ (n - x)) = 0 := by
     apply sum_eq_zero fun x hx => _
     intros x hx
-    have h : x < n := (mem_range.1 hx)
+    have h : x < n := mem_range.1 hx
     simp [tsub_eq_zero_iff_le, h]
   simp [this]
 #align polynomial.bernoulli_eval_zero Polynomial.bernoulli_eval_zero

ca3d21f7

move(Polynomial): Move out of Data (#11751)

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

56e439ec

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Ashvni Narayanan. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Ashvni Narayanan, David Loeffler
 -/
-import Mathlib.Data.Polynomial.AlgebraMap
-import Mathlib.Data.Polynomial.Derivative
+import Mathlib.Algebra.Polynomial.AlgebraMap
+import Mathlib.Algebra.Polynomial.Derivative
 import Mathlib.Data.Nat.Choose.Cast
 import Mathlib.NumberTheory.Bernoulli

ca3d21f7

chore: Rename mul-div cancellation lemmas (#11530)

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

4ea4a86a

Diff

@@ -159,7 +159,7 @@ nonrec theorem sum_bernoulli (n : ℕ) :
 theorem bernoulli_eq_sub_sum (n : ℕ) :
     (n.succ : ℚ) • bernoulli n =
       monomial n (n.succ : ℚ) - ∑ k in Finset.range n, ((n + 1).choose k : ℚ) • bernoulli k := by
-  rw [Nat.cast_succ, ← sum_bernoulli n, sum_range_succ, add_sub_cancel', choose_succ_self_right,
+  rw [Nat.cast_succ, ← sum_bernoulli n, sum_range_succ, add_sub_cancel_left, choose_succ_self_right,
     Nat.cast_succ]
 #align polynomial.bernoulli_eq_sub_sum Polynomial.bernoulli_eq_sub_sum
 
@@ -167,7 +167,7 @@ theorem bernoulli_eq_sub_sum (n : ℕ) :
 theorem sum_range_pow_eq_bernoulli_sub (n p : ℕ) :
     ((p + 1 : ℚ) * ∑ k in range n, (k : ℚ) ^ p) = (bernoulli p.succ).eval (n : ℚ) -
     _root_.bernoulli p.succ := by
-  rw [sum_range_pow, bernoulli_def, eval_finset_sum, ← sum_div, mul_div_cancel' _ _]
+  rw [sum_range_pow, bernoulli_def, eval_finset_sum, ← sum_div, mul_div_cancel₀ _ _]
   · simp_rw [eval_monomial]
     symm
     rw [← sum_flip _, sum_range_succ]

ca3d21f7

chore: Remove unnecessary "rw"s (#10704)

Remove unnecessary "rw"s.

db5a9376

Diff

@@ -108,7 +108,7 @@ theorem derivative_bernoulli_add_one (k : ℕ) :
   conv_rhs => rw [← Nat.cast_one, ← Nat.cast_add, ← C_eq_nat_cast, C_mul_monomial, mul_comm]
   rw [mul_assoc, mul_assoc, ← Nat.cast_mul, ← Nat.cast_mul]
   congr 3
-  rw [(choose_mul_succ_eq k m).symm, mul_comm]
+  rw [(choose_mul_succ_eq k m).symm]
 #align polynomial.derivative_bernoulli_add_one Polynomial.derivative_bernoulli_add_one
 
 theorem derivative_bernoulli (k : ℕ) :

ca3d21f7

chore: remove @[simp] from tsub_eq_zero_iff_le (#10474)

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

7fa9bfd0

Diff

@@ -80,7 +80,7 @@ theorem bernoulli_eval_zero (n : ℕ) : (bernoulli n).eval 0 = _root_.bernoulli
     apply sum_eq_zero fun x hx => _
     intros x hx
     have h : x < n := (mem_range.1 hx)
-    simp [h]
+    simp [tsub_eq_zero_iff_le, h]
   simp [this]
 #align polynomial.bernoulli_eval_zero Polynomial.bernoulli_eval_zero

ca3d21f7

chore(*): drop $/<| before fun (#9361)

Subset of #9319

3694e27d

Diff

@@ -77,7 +77,7 @@ theorem bernoulli_zero : bernoulli 0 = 1 := by simp [bernoulli]
 theorem bernoulli_eval_zero (n : ℕ) : (bernoulli n).eval 0 = _root_.bernoulli n := by
   rw [bernoulli, eval_finset_sum, sum_range_succ]
   have : (∑ x : ℕ in range n, _root_.bernoulli x * n.choose x * 0 ^ (n - x)) = 0 := by
-    apply sum_eq_zero <| fun x hx => _
+    apply sum_eq_zero fun x hx => _
     intros x hx
     have h : x < n := (mem_range.1 hx)
     simp [h]

ca3d21f7

chore: replace exact_mod_cast tactic with mod_cast elaborator where possible (#8404)

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

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

693fd795

Diff

@@ -115,7 +115,7 @@ theorem derivative_bernoulli (k : ℕ) :
     Polynomial.derivative (bernoulli k) = k * bernoulli (k - 1) := by
   cases k with
   | zero => rw [Nat.cast_zero, zero_mul, bernoulli_zero, derivative_one]
-  | succ k => exact_mod_cast derivative_bernoulli_add_one k
+  | succ k => exact mod_cast derivative_bernoulli_add_one k
 #align polynomial.derivative_bernoulli Polynomial.derivative_bernoulli
 
 @[simp]
@@ -238,7 +238,7 @@ theorem bernoulli_generating_function (t : A) :
   simp only [RingHom.map_sub, tsub_self, constantCoeff_one, constantCoeff_exp,
     coeff_zero_eq_constantCoeff, mul_zero, sub_self, add_zero]
   -- Let's multiply both sides by (n+1)! (OK because it's a unit)
-  have hnp1 : IsUnit ((n + 1)! : ℚ) := IsUnit.mk0 _ (by exact_mod_cast factorial_ne_zero (n + 1))
+  have hnp1 : IsUnit ((n + 1)! : ℚ) := IsUnit.mk0 _ (mod_cast factorial_ne_zero (n + 1))
   rw [← (hnp1.map (algebraMap ℚ A)).mul_right_inj]
   -- do trivial rearrangements to make RHS (n+1)*t^n
   rw [mul_left_comm, ← RingHom.map_mul]

ca3d21f7

chore: only four spaces for subsequent lines (#7286)

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

0c7d6fa5

Diff

@@ -112,7 +112,7 @@ theorem derivative_bernoulli_add_one (k : ℕ) :
 #align polynomial.derivative_bernoulli_add_one Polynomial.derivative_bernoulli_add_one
 
 theorem derivative_bernoulli (k : ℕ) :
-  Polynomial.derivative (bernoulli k) = k * bernoulli (k - 1) := by
+    Polynomial.derivative (bernoulli k) = k * bernoulli (k - 1) := by
   cases k with
   | zero => rw [Nat.cast_zero, zero_mul, bernoulli_zero, derivative_one]
   | succ k => exact_mod_cast derivative_bernoulli_add_one k

ca3d21f7

feat: fix norm num with arguments (#6600)

norm_num was passing the wrong syntax node to elabSimpArgs when elaborating, which essentially had the effect of ignoring all arguments it was passed, i.e. norm_num [add_comm] would not try to commute addition in the simp step. The fix itself is very simple (though not obvious to debug!), probably using TSyntax more would help avoid such issues in future.

Due to this bug many norm_num [blah] became rw [blah]; norm_num or similar, sometimes with porting notes, sometimes not, we fix these porting notes and other regressions during the port also.

Interestingly cancel_denoms uses norm_num [<- mul_assoc] internally, so cancel_denoms also got stronger with this change.

49a849ef

Diff

@@ -90,8 +90,7 @@ theorem bernoulli_eval_one (n : ℕ) : (bernoulli n).eval 1 = bernoulli' n := by
   simp only [← succ_eq_add_one, sum_range_succ, mul_one, cast_one, choose_self,
     (_root_.bernoulli _).mul_comm, sum_bernoulli, one_pow, mul_one, eval_C, eval_monomial, one_mul]
   by_cases h : n = 1
-  · simp [h]
-    norm_num
+  · norm_num [h]
   · simp [h]
     exact bernoulli_eq_bernoulli'_of_ne_one h
 #align polynomial.bernoulli_eval_one Polynomial.bernoulli_eval_one

ca3d21f7

chore: drop MulZeroClass. in mul_zero/zero_mul (#6682)

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).

277dea95

Diff

@@ -102,7 +102,7 @@ theorem derivative_bernoulli_add_one (k : ℕ) :
     Polynomial.derivative (bernoulli (k + 1)) = (k + 1) * bernoulli k := by
   simp_rw [bernoulli, derivative_sum, derivative_monomial, Nat.sub_sub, Nat.add_sub_add_right]
   -- LHS sum has an extra term, but the coefficient is zero:
-  rw [range_add_one, sum_insert not_mem_range_self, tsub_self, cast_zero, MulZeroClass.mul_zero,
+  rw [range_add_one, sum_insert not_mem_range_self, tsub_self, cast_zero, mul_zero,
     map_zero, zero_add, mul_sum]
   -- the rest of the sum is termwise equal:
   refine' sum_congr (by rfl) fun m _ => _
@@ -115,7 +115,7 @@ theorem derivative_bernoulli_add_one (k : ℕ) :
 theorem derivative_bernoulli (k : ℕ) :
   Polynomial.derivative (bernoulli k) = k * bernoulli (k - 1) := by
   cases k with
-  | zero => rw [Nat.cast_zero, MulZeroClass.zero_mul, bernoulli_zero, derivative_one]
+  | zero => rw [Nat.cast_zero, zero_mul, bernoulli_zero, derivative_one]
   | succ k => exact_mod_cast derivative_bernoulli_add_one k
 #align polynomial.derivative_bernoulli Polynomial.derivative_bernoulli
 
@@ -237,7 +237,7 @@ theorem bernoulli_generating_function (t : A) :
     Nat.sum_antidiagonal_eq_sum_range_succ_mk, sum_range_succ]
   -- last term is zero so kill with `add_zero`
   simp only [RingHom.map_sub, tsub_self, constantCoeff_one, constantCoeff_exp,
-    coeff_zero_eq_constantCoeff, MulZeroClass.mul_zero, sub_self, add_zero]
+    coeff_zero_eq_constantCoeff, mul_zero, sub_self, add_zero]
   -- Let's multiply both sides by (n+1)! (OK because it's a unit)
   have hnp1 : IsUnit ((n + 1)! : ℚ) := IsUnit.mk0 _ (by exact_mod_cast factorial_ne_zero (n + 1))
   rw [← (hnp1.map (algebraMap ℚ A)).mul_right_inj]

ca3d21f7

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

@@ -218,7 +218,7 @@ theorem bernoulli_eval_one_add (n : ℕ) (x : ℚ) :
 
 open PowerSeries
 
-variable {A : Type _} [CommRing A] [Algebra ℚ A]
+variable {A : Type*} [CommRing A] [Algebra ℚ A]
 
 -- TODO: define exponential generating functions, and use them here
 -- This name should probably be updated afterwards

ca3d21f7

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Ashvni Narayanan. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Ashvni Narayanan, David Loeffler
-
-! This file was ported from Lean 3 source module number_theory.bernoulli_polynomials
-! leanprover-community/mathlib commit ca3d21f7f4fd613c2a3c54ac7871163e1e5ecb3a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Polynomial.AlgebraMap
 import Mathlib.Data.Polynomial.Derivative
 import Mathlib.Data.Nat.Choose.Cast
 import Mathlib.NumberTheory.Bernoulli
 
+#align_import number_theory.bernoulli_polynomials from "leanprover-community/mathlib"@"ca3d21f7f4fd613c2a3c54ac7871163e1e5ecb3a"
+
 /-!
 # Bernoulli polynomials

ca3d21f7

chore: cleanup whitespace (#5988)

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

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

12343aa5

Diff

@@ -22,9 +22,9 @@ are an important tool obtained from Bernoulli numbers.
 ## Mathematical overview
 
 The $n$-th Bernoulli polynomial is defined as
-$$ B_n(X) = ∑_{k = 0}^n {n \choose k} (-1)^k  B_k  X^{n - k} $$
+$$ B_n(X) = ∑_{k = 0}^n {n \choose k} (-1)^k B_k X^{n - k} $$
 where $B_k$ is the $k$-th Bernoulli number. The Bernoulli polynomials are generating functions,
-$$ \frac{t  e^{tX} }{ e^t - 1} = ∑_{n = 0}^{\infty} B_n(X)  \frac{t^n}{n!} $$
+$$ \frac{t e^{tX} }{ e^t - 1} = ∑_{n = 0}^{\infty} B_n(X) \frac{t^n}{n!} $$
 
 ## Implementation detail
 
@@ -82,7 +82,7 @@ theorem bernoulli_eval_zero (n : ℕ) : (bernoulli n).eval 0 = _root_.bernoulli
   have : (∑ x : ℕ in range n, _root_.bernoulli x * n.choose x * 0 ^ (n - x)) = 0 := by
     apply sum_eq_zero <| fun x hx => _
     intros x hx
-    have h : x  <  n := (mem_range.1 hx)
+    have h : x < n := (mem_range.1 hx)
     simp [h]
   simp [this]
 #align polynomial.bernoulli_eval_zero Polynomial.bernoulli_eval_zero

ca3d21f7

chore: fix focusing dots (#5708)

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

cb02d09e

Diff

@@ -131,11 +131,11 @@ nonrec theorem sum_bernoulli (n : ℕ) :
   simp_rw [smul_monomial, mul_comm (_root_.bernoulli _) _, smul_eq_mul, ← mul_assoc]
   conv_lhs =>
     apply_congr
-    . skip
-    . conv =>
+    · skip
+    · conv =>
       apply_congr
-      . skip
-      . rw [← Nat.cast_mul, choose_mul ((le_tsub_iff_left <| mem_range_le (by assumption)).1 <|
+      · skip
+      · rw [← Nat.cast_mul, choose_mul ((le_tsub_iff_left <| mem_range_le (by assumption)).1 <|
             mem_range_le (by assumption)) (le.intro rfl),
           Nat.cast_mul, add_tsub_cancel_left, mul_assoc, mul_comm, ← smul_eq_mul, ←
           smul_monomial]
@@ -203,17 +203,17 @@ theorem bernoulli_eval_one_add (n : ℕ) (x : ℚ) :
     bernoulli_eq_sub_sum, eval_sub, eval_finset_sum]
   conv_lhs =>
     congr
-    . skip
-    . apply_congr
-      . skip
-      . rw [eval_smul, hd _ (mem_range.1 (by assumption))]
+    · skip
+    · apply_congr
+      · skip
+      · rw [eval_smul, hd _ (mem_range.1 (by assumption))]
   rw [eval_sub, eval_finset_sum]
   simp_rw [eval_smul, smul_add]
   rw [sum_add_distrib, sub_add, sub_eq_sub_iff_sub_eq_sub, _root_.add_sub_sub_cancel]
   conv_rhs =>
     congr
-    . skip
-    . congr
+    · skip
+    · congr
       rw [succ_eq_add_one, ← choose_succ_self_right d]
   rw [Nat.cast_succ, ← smul_eq_mul, ← sum_range_succ _ d, eval_monomial_one_add_sub]
   simp_rw [smul_eq_mul]

ca3d21f7

chore: re-add derivative_bernoulli (#5313)

Missed in #4352, thanks @Ruben-VandeVelde for noticing!

32533c32

Diff

@@ -102,7 +102,7 @@ theorem bernoulli_eval_one (n : ℕ) : (bernoulli n).eval 1 = bernoulli' n := by
 end Examples
 
 theorem derivative_bernoulli_add_one (k : ℕ) :
-    Polynomial.derivative (bernoulli (k + 1))= (k + 1) * bernoulli k := by
+    Polynomial.derivative (bernoulli (k + 1)) = (k + 1) * bernoulli k := by
   simp_rw [bernoulli, derivative_sum, derivative_monomial, Nat.sub_sub, Nat.add_sub_add_right]
   -- LHS sum has an extra term, but the coefficient is zero:
   rw [range_add_one, sum_insert not_mem_range_self, tsub_self, cast_zero, MulZeroClass.mul_zero,
@@ -115,6 +115,13 @@ theorem derivative_bernoulli_add_one (k : ℕ) :
   rw [(choose_mul_succ_eq k m).symm, mul_comm]
 #align polynomial.derivative_bernoulli_add_one Polynomial.derivative_bernoulli_add_one
 
+theorem derivative_bernoulli (k : ℕ) :
+  Polynomial.derivative (bernoulli k) = k * bernoulli (k - 1) := by
+  cases k with
+  | zero => rw [Nat.cast_zero, MulZeroClass.zero_mul, bernoulli_zero, derivative_one]
+  | succ k => exact_mod_cast derivative_bernoulli_add_one k
+#align polynomial.derivative_bernoulli Polynomial.derivative_bernoulli
+
 @[simp]
 nonrec theorem sum_bernoulli (n : ℕ) :
     (∑ k in range (n + 1), ((n + 1).choose k : ℚ) • bernoulli k) = monomial n (n + 1 : ℚ) := by

ca3d21f7

feat: port NumberTheory.BernoulliPolynomials (#4352)

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: Alex J Best <alex.j.best@gmail.com>

34dead3d

`number_theory.bernoulli_polynomials` ⟷ `Mathlib.NumberTheory.BernoulliPolynomials`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 560

number_theory.bernoulli_polynomials ⟷ Mathlib.NumberTheory.BernoulliPolynomials

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 560

`number_theory.bernoulli_polynomials` ⟷ `Mathlib.NumberTheory.BernoulliPolynomials`