ring_theory.polynomial.bernstein | 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

bbeb185d

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

36938f77

bump to nightly-2024-04-19-08

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

a9e81450

Diff

@@ -133,10 +133,10 @@ theorem derivative_succ_aux (n ν : ℕ) :
           ↑(n.choose (ν + 1)) * X ^ (ν + 1) * (1 - X) ^ (n - (ν + 1)))
     by
     simpa only [Polynomial.derivative_pow, ← sub_eq_add_neg, Nat.succ_sub_succ_eq_sub,
-      Polynomial.derivative_mul, Polynomial.derivative_nat_cast, MulZeroClass.zero_mul,
-      Nat.cast_add, algebraMap.coe_one, Polynomial.derivative_X, mul_one, zero_add,
-      Polynomial.derivative_sub, Polynomial.derivative_one, zero_sub, mul_neg, Nat.sub_zero, ←
-      Nat.cast_succ, Polynomial.C_eq_nat_cast]
+      Polynomial.derivative_mul, Polynomial.derivative_natCast, MulZeroClass.zero_mul, Nat.cast_add,
+      algebraMap.coe_one, Polynomial.derivative_X, mul_one, zero_add, Polynomial.derivative_sub,
+      Polynomial.derivative_one, zero_sub, mul_neg, Nat.sub_zero, ← Nat.cast_succ,
+      Polynomial.C_eq_natCast]
   conv_rhs => rw [mul_sub]
   -- We'll prove the two terms match up separately.
   refine' congr (congr_arg Sub.sub _) _
@@ -184,7 +184,7 @@ theorem iterate_derivative_at_0_eq_zero_of_lt (n : ℕ) {ν k : ℕ} :
     · simp [eval_at_0]
     · simp only [derivative_succ, Int.natCast_eq_zero, mul_eq_zero, Function.comp_apply,
         Function.iterate_succ, Polynomial.iterate_derivative_sub,
-        Polynomial.iterate_derivative_nat_cast_mul, Polynomial.eval_mul, Polynomial.eval_nat_cast,
+        Polynomial.iterate_derivative_natCast_mul, Polynomial.eval_mul, Polynomial.eval_natCast,
         Polynomial.eval_sub]
       intro h
       apply mul_eq_zero_of_right

36938f77

bump to nightly-2024-04-09-08

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

659ec6f7

Diff

@@ -389,7 +389,7 @@ theorem sum_smul (n : ℕ) : ∑ ν in Finset.range (n + 1), ν • bernsteinPol
     refine' Finset.sum_congr rfl fun k hk => (w k).trans _
     simp only [pderiv_tt_x, pderiv_tt_y, Algebra.id.smul_eq_mul, nsmul_eq_mul, e, Bool.cond_true,
       Bool.cond_false, add_zero, mul_one, MulZeroClass.mul_zero, smul_zero, MvPolynomial.aeval_X,
-      MvPolynomial.pderiv_mul, Derivation.leibniz_pow, Derivation.map_coe_nat, map_natCast, map_pow,
+      MvPolynomial.pderiv_mul, Derivation.leibniz_pow, Derivation.map_natCast, map_natCast, map_pow,
       map_mul]
   · rw [(pderiv tt).leibniz_pow, (pderiv tt).map_add, pderiv_tt_x, pderiv_tt_y]
     simp only [Algebra.id.smul_eq_mul, nsmul_eq_mul, map_natCast, map_pow, map_add, map_mul, e,
@@ -437,11 +437,11 @@ theorem sum_mul_smul (n : ℕ) :
     simp only [pderiv_tt_x, pderiv_tt_y, Algebra.id.smul_eq_mul, nsmul_eq_mul, e, Bool.cond_true,
       Bool.cond_false, add_zero, zero_add, MulZeroClass.mul_zero, smul_zero, mul_one,
       MvPolynomial.aeval_X, MvPolynomial.pderiv_X_self, MvPolynomial.pderiv_X_of_ne,
-      Derivation.leibniz_pow, Derivation.leibniz, Derivation.map_coe_nat, map_natCast, map_pow,
+      Derivation.leibniz_pow, Derivation.leibniz, Derivation.map_natCast, map_natCast, map_pow,
       map_mul, map_add]
   -- On the right hand side, we'll just simplify.
   ·
-    simp only [pderiv_one, pderiv_mul, (pderiv _).leibniz_pow, (pderiv _).map_coe_nat,
+    simp only [pderiv_one, pderiv_mul, (pderiv _).leibniz_pow, (pderiv _).map_natCast,
       (pderiv tt).map_add, pderiv_tt_x, pderiv_tt_y, Algebra.id.smul_eq_mul, add_zero, mul_one,
       Derivation.map_smul_of_tower, map_nsmul, map_pow, map_add, e, Bool.cond_true, Bool.cond_false,
       MvPolynomial.aeval_X, add_sub_cancel, one_pow, smul_smul, smul_one_mul]

36938f77

bump to nightly-2024-04-07-08

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

b03b8656

Diff

@@ -3,12 +3,12 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Data.Polynomial.Derivative
+import Algebra.Polynomial.Derivative
 import Data.Nat.Choose.Sum
 import RingTheory.Polynomial.Pochhammer
-import Data.Polynomial.AlgebraMap
+import Algebra.Polynomial.AlgebraMap
 import LinearAlgebra.LinearIndependent
-import Data.MvPolynomial.PDeriv
+import Algebra.MvPolynomial.PDeriv
 
 #align_import ring_theory.polynomial.bernstein from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"

36938f77

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -8,7 +8,7 @@ import Data.Nat.Choose.Sum
 import RingTheory.Polynomial.Pochhammer
 import Data.Polynomial.AlgebraMap
 import LinearAlgebra.LinearIndependent
-import Data.MvPolynomial.Pderiv
+import Data.MvPolynomial.PDeriv
 
 #align_import ring_theory.polynomial.bernstein from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
 
@@ -182,7 +182,7 @@ theorem iterate_derivative_at_0_eq_zero_of_lt (n : ℕ) {ν k : ℕ} :
   · rw [Nat.lt_succ_iff]
     induction' k with k ih generalizing n ν
     · simp [eval_at_0]
-    · simp only [derivative_succ, Int.coe_nat_eq_zero, mul_eq_zero, Function.comp_apply,
+    · simp only [derivative_succ, Int.natCast_eq_zero, mul_eq_zero, Function.comp_apply,
         Function.iterate_succ, Polynomial.iterate_derivative_sub,
         Polynomial.iterate_derivative_nat_cast_mul, Polynomial.eval_mul, Polynomial.eval_nat_cast,
         Polynomial.eval_sub]
@@ -236,7 +236,7 @@ theorem iterate_derivative_at_0 (n ν : ℕ) :
 theorem iterate_derivative_at_0_ne_zero [CharZero R] (n ν : ℕ) (h : ν ≤ n) :
     ((Polynomial.derivative^[ν]) (bernsteinPolynomial R n ν)).eval 0 ≠ 0 :=
   by
-  simp only [Int.coe_nat_eq_zero, bernsteinPolynomial.iterate_derivative_at_0, Ne.def,
+  simp only [Int.natCast_eq_zero, bernsteinPolynomial.iterate_derivative_at_0, Ne.def,
     Nat.cast_eq_zero]
   simp only [← ascPochhammer_eval_cast]
   norm_cast
@@ -381,7 +381,7 @@ theorem sum_smul (n : ℕ) : ∑ ν in Finset.range (n + 1), ν • bernsteinPol
       rintro (_ | k)
       · simp
       · rw [bernsteinPolynomial]
-        simp only [← nat_cast_mul, Nat.succ_eq_add_one, Nat.add_succ_sub_one, add_zero, pow_succ]
+        simp only [← nat_cast_mul, Nat.succ_eq_add_one, Nat.add_succ_sub_one, add_zero, pow_succ']
         push_cast
         ring
     rw [add_pow, (pderiv tt).map_sum, (MvPolynomial.aeval e).map_sum, Finset.sum_mul]
@@ -393,8 +393,8 @@ theorem sum_smul (n : ℕ) : ∑ ν in Finset.range (n + 1), ν • bernsteinPol
       map_mul]
   · rw [(pderiv tt).leibniz_pow, (pderiv tt).map_add, pderiv_tt_x, pderiv_tt_y]
     simp only [Algebra.id.smul_eq_mul, nsmul_eq_mul, map_natCast, map_pow, map_add, map_mul, e,
-      Bool.cond_true, Bool.cond_false, MvPolynomial.aeval_X, add_sub_cancel'_right, one_pow,
-      add_zero, mul_one]
+      Bool.cond_true, Bool.cond_false, MvPolynomial.aeval_X, add_sub_cancel, one_pow, add_zero,
+      mul_one]
 #align bernstein_polynomial.sum_smul bernsteinPolynomial.sum_smul
 -/
 
@@ -427,7 +427,7 @@ theorem sum_mul_smul (n : ℕ) :
       · simp
       · simp
       · rw [bernsteinPolynomial]
-        simp only [← nat_cast_mul, Nat.succ_eq_add_one, Nat.add_succ_sub_one, add_zero, pow_succ]
+        simp only [← nat_cast_mul, Nat.succ_eq_add_one, Nat.add_succ_sub_one, add_zero, pow_succ']
         push_cast
         ring
     rw [add_pow, (pderiv tt).map_sum, (pderiv tt).map_sum, (MvPolynomial.aeval e).map_sum,
@@ -444,7 +444,7 @@ theorem sum_mul_smul (n : ℕ) :
     simp only [pderiv_one, pderiv_mul, (pderiv _).leibniz_pow, (pderiv _).map_coe_nat,
       (pderiv tt).map_add, pderiv_tt_x, pderiv_tt_y, Algebra.id.smul_eq_mul, add_zero, mul_one,
       Derivation.map_smul_of_tower, map_nsmul, map_pow, map_add, e, Bool.cond_true, Bool.cond_false,
-      MvPolynomial.aeval_X, add_sub_cancel'_right, one_pow, smul_smul, smul_one_mul]
+      MvPolynomial.aeval_X, add_sub_cancel, one_pow, smul_smul, smul_one_mul]
 #align bernstein_polynomial.sum_mul_smul bernsteinPolynomial.sum_mul_smul
 -/

36938f77

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -222,11 +222,11 @@ theorem iterate_derivative_at_0 (n ν : ℕ) :
       · simp
       · have : n - 1 - (ν - 1) = n - ν :=
           by
-          rw [← Nat.succ_le_iff] at h'' 
+          rw [← Nat.succ_le_iff] at h''
           rw [← tsub_add_eq_tsub_tsub, add_comm, tsub_add_cancel_of_le h'']
         rw [this, ascPochhammer_eval_succ]
         rw_mod_cast [tsub_add_cancel_of_le (h'.trans n.pred_le)]
-  · simp only [not_le] at h 
+  · simp only [not_le] at h
     rw [tsub_eq_zero_iff_le.mpr (Nat.le_pred_of_lt h), eq_zero_of_lt R h]
     simp [pos_iff_ne_zero.mp (pos_of_gt h)]
 #align bernstein_polynomial.iterate_derivative_at_0 bernsteinPolynomial.iterate_derivative_at_0
@@ -243,7 +243,7 @@ theorem iterate_derivative_at_0_ne_zero [CharZero R] (n ν : ℕ) (h : ν ≤ n)
   apply ne_of_gt
   obtain rfl | h' := Nat.eq_zero_or_pos ν
   · simp
-  · rw [← Nat.succ_pred_eq_of_pos h'] at h 
+  · rw [← Nat.succ_pred_eq_of_pos h'] at h
     exact ascPochhammer_pos _ _ (tsub_pos_of_lt (Nat.lt_of_succ_le h))
 #align bernstein_polynomial.iterate_derivative_at_0_ne_zero bernsteinPolynomial.iterate_derivative_at_0_ne_zero
 -/
@@ -305,7 +305,7 @@ theorem linearIndependent_aux (n k : ℕ) (h : k ≤ n + 1) :
       -- We show that the (n-k)-th derivative at 1 doesn't vanish,
       -- but vanishes for everything in the span.
       clear ih
-      simp only [Nat.succ_eq_add_one, add_le_add_iff_right] at h 
+      simp only [Nat.succ_eq_add_one, add_le_add_iff_right] at h
       simp only [Fin.val_last, Fin.init_def]
       dsimp
       apply not_mem_span_of_apply_not_mem_span_image (@Polynomial.derivative ℚ _ ^ (n - k))

36938f77

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,12 +3,12 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.Data.Polynomial.Derivative
-import Mathbin.Data.Nat.Choose.Sum
-import Mathbin.RingTheory.Polynomial.Pochhammer
-import Mathbin.Data.Polynomial.AlgebraMap
-import Mathbin.LinearAlgebra.LinearIndependent
-import Mathbin.Data.MvPolynomial.Pderiv
+import Data.Polynomial.Derivative
+import Data.Nat.Choose.Sum
+import RingTheory.Polynomial.Pochhammer
+import Data.Polynomial.AlgebraMap
+import LinearAlgebra.LinearIndependent
+import Data.MvPolynomial.Pderiv
 
 #align_import ring_theory.polynomial.bernstein from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"

36938f77

bump to nightly-2023-09-14-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/001ffdc42920050657fd45bd2b8bfbec8eaaeb29

4e7aae4f

Diff

@@ -208,7 +208,7 @@ open Polynomial
 @[simp]
 theorem iterate_derivative_at_0 (n ν : ℕ) :
     ((Polynomial.derivative^[ν]) (bernsteinPolynomial R n ν)).eval 0 =
-      (pochhammer R ν).eval (n - (ν - 1) : ℕ) :=
+      (ascPochhammer R ν).eval (n - (ν - 1) : ℕ) :=
   by
   by_cases h : ν ≤ n
   · induction' ν with ν ih generalizing n h
@@ -217,14 +217,14 @@ theorem iterate_derivative_at_0 (n ν : ℕ) :
       simp only [derivative_succ, ih (n - 1) h', iterate_derivative_succ_at_0_eq_zero,
         Nat.succ_sub_succ_eq_sub, tsub_zero, sub_zero, iterate_derivative_sub,
         iterate_derivative_nat_cast_mul, eval_one, eval_mul, eval_add, eval_sub, eval_X, eval_comp,
-        eval_nat_cast, Function.comp_apply, Function.iterate_succ, pochhammer_succ_left]
+        eval_nat_cast, Function.comp_apply, Function.iterate_succ, ascPochhammer_succ_left]
       obtain rfl | h'' := ν.eq_zero_or_pos
       · simp
       · have : n - 1 - (ν - 1) = n - ν :=
           by
           rw [← Nat.succ_le_iff] at h'' 
           rw [← tsub_add_eq_tsub_tsub, add_comm, tsub_add_cancel_of_le h'']
-        rw [this, pochhammer_eval_succ]
+        rw [this, ascPochhammer_eval_succ]
         rw_mod_cast [tsub_add_cancel_of_le (h'.trans n.pred_le)]
   · simp only [not_le] at h 
     rw [tsub_eq_zero_iff_le.mpr (Nat.le_pred_of_lt h), eq_zero_of_lt R h]
@@ -238,13 +238,13 @@ theorem iterate_derivative_at_0_ne_zero [CharZero R] (n ν : ℕ) (h : ν ≤ n)
   by
   simp only [Int.coe_nat_eq_zero, bernsteinPolynomial.iterate_derivative_at_0, Ne.def,
     Nat.cast_eq_zero]
-  simp only [← pochhammer_eval_cast]
+  simp only [← ascPochhammer_eval_cast]
   norm_cast
   apply ne_of_gt
   obtain rfl | h' := Nat.eq_zero_or_pos ν
   · simp
   · rw [← Nat.succ_pred_eq_of_pos h'] at h 
-    exact pochhammer_pos _ _ (tsub_pos_of_lt (Nat.lt_of_succ_le h))
+    exact ascPochhammer_pos _ _ (tsub_pos_of_lt (Nat.lt_of_succ_le h))
 #align bernstein_polynomial.iterate_derivative_at_0_ne_zero bernsteinPolynomial.iterate_derivative_at_0_ne_zero
 -/
 
@@ -268,7 +268,7 @@ theorem iterate_derivative_at_1_eq_zero_of_lt (n : ℕ) {ν k : ℕ} :
 @[simp]
 theorem iterate_derivative_at_1 (n ν : ℕ) (h : ν ≤ n) :
     ((Polynomial.derivative^[n - ν]) (bernsteinPolynomial R n ν)).eval 1 =
-      (-1) ^ (n - ν) * (pochhammer R (n - ν)).eval (ν + 1) :=
+      (-1) ^ (n - ν) * (ascPochhammer R (n - ν)).eval (ν + 1) :=
   by
   rw [flip' _ _ _ h]
   simp [Polynomial.eval_comp, h]
@@ -285,8 +285,8 @@ theorem iterate_derivative_at_1_ne_zero [CharZero R] (n ν : ℕ) (h : ν ≤ n)
     ((Polynomial.derivative^[n - ν]) (bernsteinPolynomial R n ν)).eval 1 ≠ 0 :=
   by
   rw [bernsteinPolynomial.iterate_derivative_at_1 _ _ _ h, Ne.def, neg_one_pow_mul_eq_zero_iff, ←
-    Nat.cast_succ, ← pochhammer_eval_cast, ← Nat.cast_zero, Nat.cast_inj]
-  exact (pochhammer_pos _ _ (Nat.succ_pos ν)).ne'
+    Nat.cast_succ, ← ascPochhammer_eval_cast, ← Nat.cast_zero, Nat.cast_inj]
+  exact (ascPochhammer_pos _ _ (Nat.succ_pos ν)).ne'
 #align bernstein_polynomial.iterate_derivative_at_1_ne_zero bernsteinPolynomial.iterate_derivative_at_1_ne_zero
 -/

36938f77

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module ring_theory.polynomial.bernstein
-! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Polynomial.Derivative
 import Mathbin.Data.Nat.Choose.Sum
@@ -15,6 +10,8 @@ import Mathbin.Data.Polynomial.AlgebraMap
 import Mathbin.LinearAlgebra.LinearIndependent
 import Mathbin.Data.MvPolynomial.Pderiv
 
+#align_import ring_theory.polynomial.bernstein from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
+
 /-!
 # Bernstein polynomials

36938f77

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -77,10 +77,12 @@ section
 
 variable {R} {S : Type _} [CommRing S]
 
+#print bernsteinPolynomial.map /-
 @[simp]
 theorem map (f : R →+* S) (n ν : ℕ) :
     (bernsteinPolynomial R n ν).map f = bernsteinPolynomial S n ν := by simp [bernsteinPolynomial]
 #align bernstein_polynomial.map bernsteinPolynomial.map
+-/
 
 end
 
@@ -98,6 +100,7 @@ theorem flip' (n ν : ℕ) (h : ν ≤ n) :
 #align bernstein_polynomial.flip' bernsteinPolynomial.flip'
 -/
 
+#print bernsteinPolynomial.eval_at_0 /-
 theorem eval_at_0 (n ν : ℕ) : (bernsteinPolynomial R n ν).eval 0 = if ν = 0 then 1 else 0 :=
   by
   rw [bernsteinPolynomial]
@@ -105,7 +108,9 @@ theorem eval_at_0 (n ν : ℕ) : (bernsteinPolynomial R n ν).eval 0 = if ν = 0
   · subst h; simp
   · simp [zero_pow (Nat.pos_of_ne_zero h)]
 #align bernstein_polynomial.eval_at_0 bernsteinPolynomial.eval_at_0
+-/
 
+#print bernsteinPolynomial.eval_at_1 /-
 theorem eval_at_1 (n ν : ℕ) : (bernsteinPolynomial R n ν).eval 1 = if ν = n then 1 else 0 :=
   by
   rw [bernsteinPolynomial]
@@ -115,7 +120,9 @@ theorem eval_at_1 (n ν : ℕ) : (bernsteinPolynomial R n ν).eval 1 = if ν = n
     · simp [Nat.choose_eq_zero_of_lt ((tsub_eq_zero_iff_le.mp w).lt_of_ne (Ne.symm h))]
     · simp [zero_pow w]
 #align bernstein_polynomial.eval_at_1 bernsteinPolynomial.eval_at_1
+-/
 
+#print bernsteinPolynomial.derivative_succ_aux /-
 theorem derivative_succ_aux (n ν : ℕ) :
     (bernsteinPolynomial R (n + 1) (ν + 1)).derivative =
       (n + 1) * (bernsteinPolynomial R n ν - bernsteinPolynomial R n (ν + 1)) :=
@@ -149,7 +156,9 @@ theorem derivative_succ_aux (n ν : ℕ) :
       simp
     · apply mul_comm
 #align bernstein_polynomial.derivative_succ_aux bernsteinPolynomial.derivative_succ_aux
+-/
 
+#print bernsteinPolynomial.derivative_succ /-
 theorem derivative_succ (n ν : ℕ) :
     (bernsteinPolynomial R n (ν + 1)).derivative =
       n * (bernsteinPolynomial R (n - 1) ν - bernsteinPolynomial R (n - 1) (ν + 1)) :=
@@ -158,12 +167,16 @@ theorem derivative_succ (n ν : ℕ) :
   · simp [bernsteinPolynomial]
   · rw [Nat.cast_succ]; apply derivative_succ_aux
 #align bernstein_polynomial.derivative_succ bernsteinPolynomial.derivative_succ
+-/
 
+#print bernsteinPolynomial.derivative_zero /-
 theorem derivative_zero (n : ℕ) :
     (bernsteinPolynomial R n 0).derivative = -n * bernsteinPolynomial R (n - 1) 0 := by
   simp [bernsteinPolynomial, Polynomial.derivative_pow]
 #align bernstein_polynomial.derivative_zero bernsteinPolynomial.derivative_zero
+-/
 
+#print bernsteinPolynomial.iterate_derivative_at_0_eq_zero_of_lt /-
 theorem iterate_derivative_at_0_eq_zero_of_lt (n : ℕ) {ν k : ℕ} :
     k < ν → ((Polynomial.derivative^[k]) (bernsteinPolynomial R n ν)).eval 0 = 0 :=
   by
@@ -182,15 +195,19 @@ theorem iterate_derivative_at_0_eq_zero_of_lt (n : ℕ) {ν k : ℕ} :
       convert ih _ _ (Nat.pred_le_pred h)
       exact (Nat.succ_pred_eq_of_pos (k.succ_pos.trans_le h)).symm
 #align bernstein_polynomial.iterate_derivative_at_0_eq_zero_of_lt bernsteinPolynomial.iterate_derivative_at_0_eq_zero_of_lt
+-/
 
+#print bernsteinPolynomial.iterate_derivative_succ_at_0_eq_zero /-
 @[simp]
 theorem iterate_derivative_succ_at_0_eq_zero (n ν : ℕ) :
     ((Polynomial.derivative^[ν]) (bernsteinPolynomial R n (ν + 1))).eval 0 = 0 :=
   iterate_derivative_at_0_eq_zero_of_lt R n (lt_add_one ν)
 #align bernstein_polynomial.iterate_derivative_succ_at_0_eq_zero bernsteinPolynomial.iterate_derivative_succ_at_0_eq_zero
+-/
 
 open Polynomial
 
+#print bernsteinPolynomial.iterate_derivative_at_0 /-
 @[simp]
 theorem iterate_derivative_at_0 (n ν : ℕ) :
     ((Polynomial.derivative^[ν]) (bernsteinPolynomial R n ν)).eval 0 =
@@ -216,7 +233,9 @@ theorem iterate_derivative_at_0 (n ν : ℕ) :
     rw [tsub_eq_zero_iff_le.mpr (Nat.le_pred_of_lt h), eq_zero_of_lt R h]
     simp [pos_iff_ne_zero.mp (pos_of_gt h)]
 #align bernstein_polynomial.iterate_derivative_at_0 bernsteinPolynomial.iterate_derivative_at_0
+-/
 
+#print bernsteinPolynomial.iterate_derivative_at_0_ne_zero /-
 theorem iterate_derivative_at_0_ne_zero [CharZero R] (n ν : ℕ) (h : ν ≤ n) :
     ((Polynomial.derivative^[ν]) (bernsteinPolynomial R n ν)).eval 0 ≠ 0 :=
   by
@@ -230,6 +249,7 @@ theorem iterate_derivative_at_0_ne_zero [CharZero R] (n ν : ℕ) (h : ν ≤ n)
   · rw [← Nat.succ_pred_eq_of_pos h'] at h 
     exact pochhammer_pos _ _ (tsub_pos_of_lt (Nat.lt_of_succ_le h))
 #align bernstein_polynomial.iterate_derivative_at_0_ne_zero bernsteinPolynomial.iterate_derivative_at_0_ne_zero
+-/
 
 /-!
 Rather than redoing the work of evaluating the derivatives at 1,
@@ -237,6 +257,7 @@ we use the symmetry of the Bernstein polynomials.
 -/
 
 
+#print bernsteinPolynomial.iterate_derivative_at_1_eq_zero_of_lt /-
 theorem iterate_derivative_at_1_eq_zero_of_lt (n : ℕ) {ν k : ℕ} :
     k < n - ν → ((Polynomial.derivative^[k]) (bernsteinPolynomial R n ν)).eval 1 = 0 :=
   by
@@ -244,7 +265,9 @@ theorem iterate_derivative_at_1_eq_zero_of_lt (n : ℕ) {ν k : ℕ} :
   rw [flip' _ _ _ (tsub_pos_iff_lt.mp (pos_of_gt w)).le]
   simp [Polynomial.eval_comp, iterate_derivative_at_0_eq_zero_of_lt R n w]
 #align bernstein_polynomial.iterate_derivative_at_1_eq_zero_of_lt bernsteinPolynomial.iterate_derivative_at_1_eq_zero_of_lt
+-/
 
+#print bernsteinPolynomial.iterate_derivative_at_1 /-
 @[simp]
 theorem iterate_derivative_at_1 (n ν : ℕ) (h : ν ≤ n) :
     ((Polynomial.derivative^[n - ν]) (bernsteinPolynomial R n ν)).eval 1 =
@@ -258,7 +281,9 @@ theorem iterate_derivative_at_1 (n ν : ℕ) (h : ν ≤ n) :
     norm_cast
     rw [← tsub_add_eq_tsub_tsub, tsub_tsub_cancel_of_le (nat.succ_le_iff.mpr h')]
 #align bernstein_polynomial.iterate_derivative_at_1 bernsteinPolynomial.iterate_derivative_at_1
+-/
 
+#print bernsteinPolynomial.iterate_derivative_at_1_ne_zero /-
 theorem iterate_derivative_at_1_ne_zero [CharZero R] (n ν : ℕ) (h : ν ≤ n) :
     ((Polynomial.derivative^[n - ν]) (bernsteinPolynomial R n ν)).eval 1 ≠ 0 :=
   by
@@ -266,6 +291,7 @@ theorem iterate_derivative_at_1_ne_zero [CharZero R] (n ν : ℕ) (h : ν ≤ n)
     Nat.cast_succ, ← pochhammer_eval_cast, ← Nat.cast_zero, Nat.cast_inj]
   exact (pochhammer_pos _ _ (Nat.succ_pos ν)).ne'
 #align bernstein_polynomial.iterate_derivative_at_1_ne_zero bernsteinPolynomial.iterate_derivative_at_1_ne_zero
+-/
 
 open Submodule
 
@@ -333,6 +359,7 @@ open Polynomial
 
 open MvPolynomial
 
+#print bernsteinPolynomial.sum_smul /-
 theorem sum_smul (n : ℕ) : ∑ ν in Finset.range (n + 1), ν • bernsteinPolynomial R n ν = n • X :=
   by
   -- We calculate the `x`-derivative of `(x+y)^n`, evaluated at `y=(1-x)`,
@@ -372,7 +399,9 @@ theorem sum_smul (n : ℕ) : ∑ ν in Finset.range (n + 1), ν • bernsteinPol
       Bool.cond_true, Bool.cond_false, MvPolynomial.aeval_X, add_sub_cancel'_right, one_pow,
       add_zero, mul_one]
 #align bernstein_polynomial.sum_smul bernsteinPolynomial.sum_smul
+-/
 
+#print bernsteinPolynomial.sum_mul_smul /-
 theorem sum_mul_smul (n : ℕ) :
     ∑ ν in Finset.range (n + 1), (ν * (ν - 1)) • bernsteinPolynomial R n ν =
       (n * (n - 1)) • X ^ 2 :=
@@ -420,7 +449,9 @@ theorem sum_mul_smul (n : ℕ) :
       Derivation.map_smul_of_tower, map_nsmul, map_pow, map_add, e, Bool.cond_true, Bool.cond_false,
       MvPolynomial.aeval_X, add_sub_cancel'_right, one_pow, smul_smul, smul_one_mul]
 #align bernstein_polynomial.sum_mul_smul bernsteinPolynomial.sum_mul_smul
+-/
 
+#print bernsteinPolynomial.variance /-
 /-- A certain linear combination of the previous three identities,
 which we'll want later.
 -/
@@ -455,6 +486,7 @@ theorem variance (n : ℕ) :
     · simp
     · simp; ring
 #align bernstein_polynomial.variance bernsteinPolynomial.variance
+-/
 
 end bernsteinPolynomial

36938f77

bump to nightly-2023-06-10-07

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

3fdc57bc

Diff

@@ -321,9 +321,9 @@ theorem linearIndependent (n : ℕ) :
 -/
 
 #print bernsteinPolynomial.sum /-
-theorem sum (n : ℕ) : (∑ ν in Finset.range (n + 1), bernsteinPolynomial R n ν) = 1 :=
+theorem sum (n : ℕ) : ∑ ν in Finset.range (n + 1), bernsteinPolynomial R n ν = 1 :=
   calc
-    (∑ ν in Finset.range (n + 1), bernsteinPolynomial R n ν) = (X + (1 - X)) ^ n := by rw [add_pow];
+    ∑ ν in Finset.range (n + 1), bernsteinPolynomial R n ν = (X + (1 - X)) ^ n := by rw [add_pow];
       simp only [bernsteinPolynomial, mul_comm, mul_assoc, mul_left_comm]
     _ = 1 := by simp
 #align bernstein_polynomial.sum bernsteinPolynomial.sum
@@ -333,7 +333,7 @@ open Polynomial
 
 open MvPolynomial
 
-theorem sum_smul (n : ℕ) : (∑ ν in Finset.range (n + 1), ν • bernsteinPolynomial R n ν) = n • X :=
+theorem sum_smul (n : ℕ) : ∑ ν in Finset.range (n + 1), ν • bernsteinPolynomial R n ν = n • X :=
   by
   -- We calculate the `x`-derivative of `(x+y)^n`, evaluated at `y=(1-x)`,
   -- either directly or by using the binomial theorem.
@@ -374,7 +374,7 @@ theorem sum_smul (n : ℕ) : (∑ ν in Finset.range (n + 1), ν • bernsteinPo
 #align bernstein_polynomial.sum_smul bernsteinPolynomial.sum_smul
 
 theorem sum_mul_smul (n : ℕ) :
-    (∑ ν in Finset.range (n + 1), (ν * (ν - 1)) • bernsteinPolynomial R n ν) =
+    ∑ ν in Finset.range (n + 1), (ν * (ν - 1)) • bernsteinPolynomial R n ν =
       (n * (n - 1)) • X ^ 2 :=
   by
   -- We calculate the second `x`-derivative of `(x+y)^n`, evaluated at `y=(1-x)`,
@@ -425,7 +425,7 @@ theorem sum_mul_smul (n : ℕ) :
 which we'll want later.
 -/
 theorem variance (n : ℕ) :
-    (∑ ν in Finset.range (n + 1), (n • Polynomial.X - ν) ^ 2 * bernsteinPolynomial R n ν) =
+    ∑ ν in Finset.range (n + 1), (n • Polynomial.X - ν) ^ 2 * bernsteinPolynomial R n ν =
       n • Polynomial.X * (1 - Polynomial.X) :=
   by
   have p :

36938f77

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -326,7 +326,6 @@ theorem sum (n : ℕ) : (∑ ν in Finset.range (n + 1), bernsteinPolynomial R n
     (∑ ν in Finset.range (n + 1), bernsteinPolynomial R n ν) = (X + (1 - X)) ^ n := by rw [add_pow];
       simp only [bernsteinPolynomial, mul_comm, mul_assoc, mul_left_comm]
     _ = 1 := by simp
-    
 #align bernstein_polynomial.sum bernsteinPolynomial.sum
 -/
 
@@ -449,7 +448,6 @@ theorem variance (n : ℕ) :
     _ = _ := Finset.sum_congr rfl fun k m => _
     _ = _ := p
     _ = _ := _
-    
   · congr 1; simp only [← nat_cast_mul, push_cast]
     cases k <;> · simp; ring
   · simp only [← nat_cast_mul, push_cast]

36938f77

bump to nightly-2023-06-07-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3

831e78ce

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module ring_theory.polynomial.bernstein
-! leanprover-community/mathlib commit bbeb185db4ccee8ed07dc48449414ebfa39cb821
+! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.Data.MvPolynomial.Pderiv
 /-!
 # Bernstein polynomials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The definition of the Bernstein polynomials
 ```
 bernstein_polynomial (R : Type*) [comm_ring R] (n ν : ℕ) : R[X] :=

bbeb185d

bump to nightly-2023-06-05-12

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

d07076be

Diff

@@ -47,6 +47,7 @@ open scoped BigOperators Polynomial
 
 variable (R : Type _) [CommRing R]
 
+#print bernsteinPolynomial /-
 /-- `bernstein_polynomial R n ν` is `(choose n ν) * X^ν * (1 - X)^(n - ν)`.
 
 Although the coefficients are integers, it is convenient to work over an arbitrary commutative ring.
@@ -54,6 +55,7 @@ Although the coefficients are integers, it is convenient to work over an arbitra
 def bernsteinPolynomial (n ν : ℕ) : R[X] :=
   choose n ν * X ^ ν * (1 - X) ^ (n - ν)
 #align bernstein_polynomial bernsteinPolynomial
+-/
 
 example : bernsteinPolynomial ℤ 3 2 = 3 * X ^ 2 - 3 * X ^ 3 :=
   by
@@ -62,9 +64,11 @@ example : bernsteinPolynomial ℤ 3 2 = 3 * X ^ 2 - 3 * X ^ 3 :=
 
 namespace bernsteinPolynomial
 
+#print bernsteinPolynomial.eq_zero_of_lt /-
 theorem eq_zero_of_lt {n ν : ℕ} (h : n < ν) : bernsteinPolynomial R n ν = 0 := by
   simp [bernsteinPolynomial, Nat.choose_eq_zero_of_lt h]
 #align bernstein_polynomial.eq_zero_of_lt bernsteinPolynomial.eq_zero_of_lt
+-/
 
 section
 
@@ -77,15 +81,19 @@ theorem map (f : R →+* S) (n ν : ℕ) :
 
 end
 
+#print bernsteinPolynomial.flip /-
 theorem flip (n ν : ℕ) (h : ν ≤ n) :
     (bernsteinPolynomial R n ν).comp (1 - X) = bernsteinPolynomial R n (n - ν) := by
   simp [bernsteinPolynomial, h, tsub_tsub_assoc, mul_right_comm]
 #align bernstein_polynomial.flip bernsteinPolynomial.flip
+-/
 
+#print bernsteinPolynomial.flip' /-
 theorem flip' (n ν : ℕ) (h : ν ≤ n) :
     bernsteinPolynomial R n ν = (bernsteinPolynomial R n (n - ν)).comp (1 - X) := by
   simp [← flip _ _ _ h, Polynomial.comp_assoc]
 #align bernstein_polynomial.flip' bernsteinPolynomial.flip'
+-/
 
 theorem eval_at_0 (n ν : ℕ) : (bernsteinPolynomial R n ν).eval 0 = if ν = 0 then 1 else 0 :=
   by
@@ -258,6 +266,7 @@ theorem iterate_derivative_at_1_ne_zero [CharZero R] (n ν : ℕ) (h : ν ≤ n)
 
 open Submodule
 
+#print bernsteinPolynomial.linearIndependent_aux /-
 theorem linearIndependent_aux (n k : ℕ) (h : k ≤ n + 1) :
     LinearIndependent ℚ fun ν : Fin k => bernsteinPolynomial ℚ n ν :=
   by
@@ -292,7 +301,9 @@ theorem linearIndependent_aux (n k : ℕ) (h : k ≤ n + 1) :
       · intro x y hx hy; simp [hx, hy]
       · intro a x h; simp [h]
 #align bernstein_polynomial.linear_independent_aux bernsteinPolynomial.linearIndependent_aux
+-/
 
+#print bernsteinPolynomial.linearIndependent /-
 /-- The Bernstein polynomials are linearly independent.
 
 We prove by induction that the collection of `bernstein_polynomial n ν` for `ν = 0, ..., k`
@@ -304,7 +315,9 @@ theorem linearIndependent (n : ℕ) :
     LinearIndependent ℚ fun ν : Fin (n + 1) => bernsteinPolynomial ℚ n ν :=
   linearIndependent_aux n (n + 1) le_rfl
 #align bernstein_polynomial.linear_independent bernsteinPolynomial.linearIndependent
+-/
 
+#print bernsteinPolynomial.sum /-
 theorem sum (n : ℕ) : (∑ ν in Finset.range (n + 1), bernsteinPolynomial R n ν) = 1 :=
   calc
     (∑ ν in Finset.range (n + 1), bernsteinPolynomial R n ν) = (X + (1 - X)) ^ n := by rw [add_pow];
@@ -312,6 +325,7 @@ theorem sum (n : ℕ) : (∑ ν in Finset.range (n + 1), bernsteinPolynomial R n
     _ = 1 := by simp
     
 #align bernstein_polynomial.sum bernsteinPolynomial.sum
+-/
 
 open Polynomial

bbeb185d

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -133,7 +133,7 @@ theorem derivative_succ_aux (n ν : ℕ) :
     rw [mul_comm, ← mul_assoc, ← mul_assoc]; congr 1
     norm_cast
     congr 1
-    convert(Nat.choose_mul_succ_eq n (ν + 1)).symm using 1
+    convert (Nat.choose_mul_succ_eq n (ν + 1)).symm using 1
     · convert mul_comm _ _ using 2
       simp
     · apply mul_comm
@@ -394,7 +394,7 @@ theorem sum_mul_smul (n : ℕ) :
     refine' Finset.sum_congr rfl fun k hk => (w k).trans _
     simp only [pderiv_tt_x, pderiv_tt_y, Algebra.id.smul_eq_mul, nsmul_eq_mul, e, Bool.cond_true,
       Bool.cond_false, add_zero, zero_add, MulZeroClass.mul_zero, smul_zero, mul_one,
-      MvPolynomial.aeval_X, MvPolynomial.pderiv_x_self, MvPolynomial.pderiv_x_of_ne,
+      MvPolynomial.aeval_X, MvPolynomial.pderiv_X_self, MvPolynomial.pderiv_X_of_ne,
       Derivation.leibniz_pow, Derivation.leibniz, Derivation.map_coe_nat, map_natCast, map_pow,
       map_mul, map_add]
   -- On the right hand side, we'll just simplify.

bbeb185d

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -197,11 +197,11 @@ theorem iterate_derivative_at_0 (n ν : ℕ) :
       · simp
       · have : n - 1 - (ν - 1) = n - ν :=
           by
-          rw [← Nat.succ_le_iff] at h''
+          rw [← Nat.succ_le_iff] at h'' 
           rw [← tsub_add_eq_tsub_tsub, add_comm, tsub_add_cancel_of_le h'']
         rw [this, pochhammer_eval_succ]
         rw_mod_cast [tsub_add_cancel_of_le (h'.trans n.pred_le)]
-  · simp only [not_le] at h
+  · simp only [not_le] at h 
     rw [tsub_eq_zero_iff_le.mpr (Nat.le_pred_of_lt h), eq_zero_of_lt R h]
     simp [pos_iff_ne_zero.mp (pos_of_gt h)]
 #align bernstein_polynomial.iterate_derivative_at_0 bernsteinPolynomial.iterate_derivative_at_0
@@ -216,7 +216,7 @@ theorem iterate_derivative_at_0_ne_zero [CharZero R] (n ν : ℕ) (h : ν ≤ n)
   apply ne_of_gt
   obtain rfl | h' := Nat.eq_zero_or_pos ν
   · simp
-  · rw [← Nat.succ_pred_eq_of_pos h'] at h
+  · rw [← Nat.succ_pred_eq_of_pos h'] at h 
     exact pochhammer_pos _ _ (tsub_pos_of_lt (Nat.lt_of_succ_le h))
 #align bernstein_polynomial.iterate_derivative_at_0_ne_zero bernsteinPolynomial.iterate_derivative_at_0_ne_zero
 
@@ -270,7 +270,7 @@ theorem linearIndependent_aux (n k : ℕ) (h : k ≤ n + 1) :
       -- We show that the (n-k)-th derivative at 1 doesn't vanish,
       -- but vanishes for everything in the span.
       clear ih
-      simp only [Nat.succ_eq_add_one, add_le_add_iff_right] at h
+      simp only [Nat.succ_eq_add_one, add_le_add_iff_right] at h 
       simp only [Fin.val_last, Fin.init_def]
       dsimp
       apply not_mem_span_of_apply_not_mem_span_image (@Polynomial.derivative ℚ _ ^ (n - k))

bbeb185d

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -43,7 +43,7 @@ open Nat (choose)
 
 open Polynomial (X)
 
-open BigOperators Polynomial
+open scoped BigOperators Polynomial
 
 variable (R : Type _) [CommRing R]

bbeb185d

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -91,8 +91,7 @@ theorem eval_at_0 (n ν : ℕ) : (bernsteinPolynomial R n ν).eval 0 = if ν = 0
   by
   rw [bernsteinPolynomial]
   split_ifs
-  · subst h
-    simp
+  · subst h; simp
   · simp [zero_pow (Nat.pos_of_ne_zero h)]
 #align bernstein_polynomial.eval_at_0 bernsteinPolynomial.eval_at_0
 
@@ -100,8 +99,7 @@ theorem eval_at_1 (n ν : ℕ) : (bernsteinPolynomial R n ν).eval 1 = if ν = n
   by
   rw [bernsteinPolynomial]
   split_ifs
-  · subst h
-    simp
+  · subst h; simp
   · obtain w | w := (n - ν).eq_zero_or_pos
     · simp [Nat.choose_eq_zero_of_lt ((tsub_eq_zero_iff_le.mp w).lt_of_ne (Ne.symm h))]
     · simp [zero_pow w]
@@ -131,10 +129,8 @@ theorem derivative_succ_aux (n ν : ℕ) :
     refine' congr (congr_arg (· * ·) (congr (congr_arg (· * ·) _) rfl)) rfl
     -- Now it's just about binomial coefficients
     exact_mod_cast congr_arg (fun m : ℕ => (m : R[X])) (Nat.succ_mul_choose_eq n ν).symm
-  · rw [← tsub_add_eq_tsub_tsub, ← mul_assoc, ← mul_assoc]
-    congr 1
-    rw [mul_comm, ← mul_assoc, ← mul_assoc]
-    congr 1
+  · rw [← tsub_add_eq_tsub_tsub, ← mul_assoc, ← mul_assoc]; congr 1
+    rw [mul_comm, ← mul_assoc, ← mul_assoc]; congr 1
     norm_cast
     congr 1
     convert(Nat.choose_mul_succ_eq n (ν + 1)).symm using 1
@@ -149,8 +145,7 @@ theorem derivative_succ (n ν : ℕ) :
   by
   cases n
   · simp [bernsteinPolynomial]
-  · rw [Nat.cast_succ]
-    apply derivative_succ_aux
+  · rw [Nat.cast_succ]; apply derivative_succ_aux
 #align bernstein_polynomial.derivative_succ bernsteinPolynomial.derivative_succ
 
 theorem derivative_zero (n : ℕ) :
@@ -291,14 +286,11 @@ theorem linearIndependent_aux (n k : ℕ) (h : k ≤ n + 1) :
         exact (iterate_derivative_at_1_ne_zero ℚ n k h).symm
       apply span_induction m
       · simp
-        rintro ⟨a, w⟩
-        simp only [Fin.val_mk]
+        rintro ⟨a, w⟩; simp only [Fin.val_mk]
         rw [iterate_derivative_at_1_eq_zero_of_lt ℚ n ((tsub_lt_tsub_iff_left_of_le h).mpr w)]
       · simp
-      · intro x y hx hy
-        simp [hx, hy]
-      · intro a x h
-        simp [h]
+      · intro x y hx hy; simp [hx, hy]
+      · intro a x h; simp [h]
 #align bernstein_polynomial.linear_independent_aux bernsteinPolynomial.linearIndependent_aux
 
 /-- The Bernstein polynomials are linearly independent.
@@ -315,9 +307,7 @@ theorem linearIndependent (n : ℕ) :
 
 theorem sum (n : ℕ) : (∑ ν in Finset.range (n + 1), bernsteinPolynomial R n ν) = 1 :=
   calc
-    (∑ ν in Finset.range (n + 1), bernsteinPolynomial R n ν) = (X + (1 - X)) ^ n :=
-      by
-      rw [add_pow]
+    (∑ ν in Finset.range (n + 1), bernsteinPolynomial R n ν) = (X + (1 - X)) ^ n := by rw [add_pow];
       simp only [bernsteinPolynomial, mul_comm, mul_assoc, mul_left_comm]
     _ = 1 := by simp
     
@@ -334,12 +324,8 @@ theorem sum_smul (n : ℕ) : (∑ ν in Finset.range (n + 1), ν • bernsteinPo
   -- We'll work in `mv_polynomial bool R`.
   let x : MvPolynomial Bool R := MvPolynomial.X tt
   let y : MvPolynomial Bool R := MvPolynomial.X ff
-  have pderiv_tt_x : pderiv tt x = 1 := by
-    rw [pderiv_X]
-    rfl
-  have pderiv_tt_y : pderiv tt y = 0 := by
-    rw [pderiv_X]
-    rfl
+  have pderiv_tt_x : pderiv tt x = 1 := by rw [pderiv_X]; rfl
+  have pderiv_tt_y : pderiv tt y = 0 := by rw [pderiv_X]; rfl
   let e : Bool → R[X] := fun i => cond i X (1 - X)
   -- Start with `(x+y)^n = (x+y)^n`,
   -- take the `x`-derivative, evaluate at `x=X, y=1-X`, and multiply by `X`:
@@ -380,12 +366,8 @@ theorem sum_mul_smul (n : ℕ) :
   -- We'll work in `mv_polynomial bool R`.
   let x : MvPolynomial Bool R := MvPolynomial.X tt
   let y : MvPolynomial Bool R := MvPolynomial.X ff
-  have pderiv_tt_x : pderiv tt x = 1 := by
-    rw [pderiv_X]
-    rfl
-  have pderiv_tt_y : pderiv tt y = 0 := by
-    rw [pderiv_X]
-    rfl
+  have pderiv_tt_x : pderiv tt x = 1 := by rw [pderiv_X]; rfl
+  have pderiv_tt_y : pderiv tt y = 0 := by rw [pderiv_X]; rfl
   let e : Bool → R[X] := fun i => cond i X (1 - X)
   -- Start with `(x+y)^n = (x+y)^n`,
   -- take the second `x`-derivative, evaluate at `x=X, y=1-X`, and multiply by `X`:
@@ -451,16 +433,12 @@ theorem variance (n : ℕ) :
     _ = _ := p
     _ = _ := _
     
-  · congr 1
-    simp only [← nat_cast_mul, push_cast]
-    cases k <;>
-      · simp
-        ring
+  · congr 1; simp only [← nat_cast_mul, push_cast]
+    cases k <;> · simp; ring
   · simp only [← nat_cast_mul, push_cast]
     cases n
     · simp
-    · simp
-      ring
+    · simp; ring
 #align bernstein_polynomial.variance bernsteinPolynomial.variance
 
 end bernsteinPolynomial

bbeb185d

bump to nightly-2023-03-17-00

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

c85864d4

Diff

@@ -137,7 +137,7 @@ theorem derivative_succ_aux (n ν : ℕ) :
     congr 1
     norm_cast
     congr 1
-    convert (Nat.choose_mul_succ_eq n (ν + 1)).symm using 1
+    convert(Nat.choose_mul_succ_eq n (ν + 1)).symm using 1
     · convert mul_comm _ _ using 2
       simp
     · apply mul_comm

bbeb185d

bump to nightly-2023-03-15-10

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

f73428b0

Diff

@@ -327,13 +327,13 @@ open Polynomial
 
 open MvPolynomial
 
-theorem sum_smul (n : ℕ) : (∑ ν in Finset.range (n + 1), ν • bernsteinPolynomial R n ν) = n • x :=
+theorem sum_smul (n : ℕ) : (∑ ν in Finset.range (n + 1), ν • bernsteinPolynomial R n ν) = n • X :=
   by
   -- We calculate the `x`-derivative of `(x+y)^n`, evaluated at `y=(1-x)`,
   -- either directly or by using the binomial theorem.
   -- We'll work in `mv_polynomial bool R`.
-  let x : MvPolynomial Bool R := MvPolynomial.x tt
-  let y : MvPolynomial Bool R := MvPolynomial.x ff
+  let x : MvPolynomial Bool R := MvPolynomial.X tt
+  let y : MvPolynomial Bool R := MvPolynomial.X ff
   have pderiv_tt_x : pderiv tt x = 1 := by
     rw [pderiv_X]
     rfl
@@ -362,24 +362,24 @@ theorem sum_smul (n : ℕ) : (∑ ν in Finset.range (n + 1), ν • bernsteinPo
     -- Step inside the sum:
     refine' Finset.sum_congr rfl fun k hk => (w k).trans _
     simp only [pderiv_tt_x, pderiv_tt_y, Algebra.id.smul_eq_mul, nsmul_eq_mul, e, Bool.cond_true,
-      Bool.cond_false, add_zero, mul_one, MulZeroClass.mul_zero, smul_zero, MvPolynomial.aeval_x,
+      Bool.cond_false, add_zero, mul_one, MulZeroClass.mul_zero, smul_zero, MvPolynomial.aeval_X,
       MvPolynomial.pderiv_mul, Derivation.leibniz_pow, Derivation.map_coe_nat, map_natCast, map_pow,
       map_mul]
   · rw [(pderiv tt).leibniz_pow, (pderiv tt).map_add, pderiv_tt_x, pderiv_tt_y]
     simp only [Algebra.id.smul_eq_mul, nsmul_eq_mul, map_natCast, map_pow, map_add, map_mul, e,
-      Bool.cond_true, Bool.cond_false, MvPolynomial.aeval_x, add_sub_cancel'_right, one_pow,
+      Bool.cond_true, Bool.cond_false, MvPolynomial.aeval_X, add_sub_cancel'_right, one_pow,
       add_zero, mul_one]
 #align bernstein_polynomial.sum_smul bernsteinPolynomial.sum_smul
 
 theorem sum_mul_smul (n : ℕ) :
     (∑ ν in Finset.range (n + 1), (ν * (ν - 1)) • bernsteinPolynomial R n ν) =
-      (n * (n - 1)) • x ^ 2 :=
+      (n * (n - 1)) • X ^ 2 :=
   by
   -- We calculate the second `x`-derivative of `(x+y)^n`, evaluated at `y=(1-x)`,
   -- either directly or by using the binomial theorem.
   -- We'll work in `mv_polynomial bool R`.
-  let x : MvPolynomial Bool R := MvPolynomial.x tt
-  let y : MvPolynomial Bool R := MvPolynomial.x ff
+  let x : MvPolynomial Bool R := MvPolynomial.X tt
+  let y : MvPolynomial Bool R := MvPolynomial.X ff
   have pderiv_tt_x : pderiv tt x = 1 := by
     rw [pderiv_X]
     rfl
@@ -412,7 +412,7 @@ theorem sum_mul_smul (n : ℕ) :
     refine' Finset.sum_congr rfl fun k hk => (w k).trans _
     simp only [pderiv_tt_x, pderiv_tt_y, Algebra.id.smul_eq_mul, nsmul_eq_mul, e, Bool.cond_true,
       Bool.cond_false, add_zero, zero_add, MulZeroClass.mul_zero, smul_zero, mul_one,
-      MvPolynomial.aeval_x, MvPolynomial.pderiv_x_self, MvPolynomial.pderiv_x_of_ne,
+      MvPolynomial.aeval_X, MvPolynomial.pderiv_x_self, MvPolynomial.pderiv_x_of_ne,
       Derivation.leibniz_pow, Derivation.leibniz, Derivation.map_coe_nat, map_natCast, map_pow,
       map_mul, map_add]
   -- On the right hand side, we'll just simplify.
@@ -420,7 +420,7 @@ theorem sum_mul_smul (n : ℕ) :
     simp only [pderiv_one, pderiv_mul, (pderiv _).leibniz_pow, (pderiv _).map_coe_nat,
       (pderiv tt).map_add, pderiv_tt_x, pderiv_tt_y, Algebra.id.smul_eq_mul, add_zero, mul_one,
       Derivation.map_smul_of_tower, map_nsmul, map_pow, map_add, e, Bool.cond_true, Bool.cond_false,
-      MvPolynomial.aeval_x, add_sub_cancel'_right, one_pow, smul_smul, smul_one_mul]
+      MvPolynomial.aeval_X, add_sub_cancel'_right, one_pow, smul_smul, smul_one_mul]
 #align bernstein_polynomial.sum_mul_smul bernsteinPolynomial.sum_mul_smul
 
 /-- A certain linear combination of the previous three identities,

bbeb185d

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -120,10 +120,10 @@ theorem derivative_succ_aux (n ν : ℕ) :
           ↑(n.choose (ν + 1)) * X ^ (ν + 1) * (1 - X) ^ (n - (ν + 1)))
     by
     simpa only [Polynomial.derivative_pow, ← sub_eq_add_neg, Nat.succ_sub_succ_eq_sub,
-      Polynomial.derivative_mul, Polynomial.derivative_nat_cast, zero_mul, Nat.cast_add,
-      algebraMap.coe_one, Polynomial.derivative_X, mul_one, zero_add, Polynomial.derivative_sub,
-      Polynomial.derivative_one, zero_sub, mul_neg, Nat.sub_zero, ← Nat.cast_succ,
-      Polynomial.C_eq_nat_cast]
+      Polynomial.derivative_mul, Polynomial.derivative_nat_cast, MulZeroClass.zero_mul,
+      Nat.cast_add, algebraMap.coe_one, Polynomial.derivative_X, mul_one, zero_add,
+      Polynomial.derivative_sub, Polynomial.derivative_one, zero_sub, mul_neg, Nat.sub_zero, ←
+      Nat.cast_succ, Polynomial.C_eq_nat_cast]
   conv_rhs => rw [mul_sub]
   -- We'll prove the two terms match up separately.
   refine' congr (congr_arg Sub.sub _) _
@@ -362,7 +362,7 @@ theorem sum_smul (n : ℕ) : (∑ ν in Finset.range (n + 1), ν • bernsteinPo
     -- Step inside the sum:
     refine' Finset.sum_congr rfl fun k hk => (w k).trans _
     simp only [pderiv_tt_x, pderiv_tt_y, Algebra.id.smul_eq_mul, nsmul_eq_mul, e, Bool.cond_true,
-      Bool.cond_false, add_zero, mul_one, mul_zero, smul_zero, MvPolynomial.aeval_x,
+      Bool.cond_false, add_zero, mul_one, MulZeroClass.mul_zero, smul_zero, MvPolynomial.aeval_x,
       MvPolynomial.pderiv_mul, Derivation.leibniz_pow, Derivation.map_coe_nat, map_natCast, map_pow,
       map_mul]
   · rw [(pderiv tt).leibniz_pow, (pderiv tt).map_add, pderiv_tt_x, pderiv_tt_y]
@@ -411,9 +411,10 @@ theorem sum_mul_smul (n : ℕ) :
     -- Step inside the sum:
     refine' Finset.sum_congr rfl fun k hk => (w k).trans _
     simp only [pderiv_tt_x, pderiv_tt_y, Algebra.id.smul_eq_mul, nsmul_eq_mul, e, Bool.cond_true,
-      Bool.cond_false, add_zero, zero_add, mul_zero, smul_zero, mul_one, MvPolynomial.aeval_x,
-      MvPolynomial.pderiv_x_self, MvPolynomial.pderiv_x_of_ne, Derivation.leibniz_pow,
-      Derivation.leibniz, Derivation.map_coe_nat, map_natCast, map_pow, map_mul, map_add]
+      Bool.cond_false, add_zero, zero_add, MulZeroClass.mul_zero, smul_zero, mul_one,
+      MvPolynomial.aeval_x, MvPolynomial.pderiv_x_self, MvPolynomial.pderiv_x_of_ne,
+      Derivation.leibniz_pow, Derivation.leibniz, Derivation.map_coe_nat, map_natCast, map_pow,
+      map_mul, map_add]
   -- On the right hand side, we'll just simplify.
   ·
     simp only [pderiv_one, pderiv_mul, (pderiv _).leibniz_pow, (pderiv _).map_coe_nat,

bbeb185d

bump to nightly-2023-03-09-12

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

ca1d663b

Diff

@@ -121,7 +121,7 @@ theorem derivative_succ_aux (n ν : ℕ) :
     by
     simpa only [Polynomial.derivative_pow, ← sub_eq_add_neg, Nat.succ_sub_succ_eq_sub,
       Polynomial.derivative_mul, Polynomial.derivative_nat_cast, zero_mul, Nat.cast_add,
-      algebraMap.coe_one, Polynomial.derivative_x, mul_one, zero_add, Polynomial.derivative_sub,
+      algebraMap.coe_one, Polynomial.derivative_X, mul_one, zero_add, Polynomial.derivative_sub,
       Polynomial.derivative_one, zero_sub, mul_neg, Nat.sub_zero, ← Nat.cast_succ,
       Polynomial.C_eq_nat_cast]
   conv_rhs => rw [mul_sub]

bbeb185d

bump to nightly-2023-03-08-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

422cc012

Diff

@@ -41,7 +41,7 @@ noncomputable section
 
 open Nat (choose)
 
-open Polynomial (x)
+open Polynomial (X)
 
 open BigOperators Polynomial
 
@@ -52,10 +52,10 @@ variable (R : Type _) [CommRing R]
 Although the coefficients are integers, it is convenient to work over an arbitrary commutative ring.
 -/
 def bernsteinPolynomial (n ν : ℕ) : R[X] :=
-  choose n ν * x ^ ν * (1 - x) ^ (n - ν)
+  choose n ν * X ^ ν * (1 - X) ^ (n - ν)
 #align bernstein_polynomial bernsteinPolynomial
 
-example : bernsteinPolynomial ℤ 3 2 = 3 * x ^ 2 - 3 * x ^ 3 :=
+example : bernsteinPolynomial ℤ 3 2 = 3 * X ^ 2 - 3 * X ^ 3 :=
   by
   norm_num [bernsteinPolynomial, choose]
   ring
@@ -78,12 +78,12 @@ theorem map (f : R →+* S) (n ν : ℕ) :
 end
 
 theorem flip (n ν : ℕ) (h : ν ≤ n) :
-    (bernsteinPolynomial R n ν).comp (1 - x) = bernsteinPolynomial R n (n - ν) := by
+    (bernsteinPolynomial R n ν).comp (1 - X) = bernsteinPolynomial R n (n - ν) := by
   simp [bernsteinPolynomial, h, tsub_tsub_assoc, mul_right_comm]
 #align bernstein_polynomial.flip bernsteinPolynomial.flip
 
 theorem flip' (n ν : ℕ) (h : ν ≤ n) :
-    bernsteinPolynomial R n ν = (bernsteinPolynomial R n (n - ν)).comp (1 - x) := by
+    bernsteinPolynomial R n ν = (bernsteinPolynomial R n (n - ν)).comp (1 - X) := by
   simp [← flip _ _ _ h, Polynomial.comp_assoc]
 #align bernstein_polynomial.flip' bernsteinPolynomial.flip'
 
@@ -123,7 +123,7 @@ theorem derivative_succ_aux (n ν : ℕ) :
       Polynomial.derivative_mul, Polynomial.derivative_nat_cast, zero_mul, Nat.cast_add,
       algebraMap.coe_one, Polynomial.derivative_x, mul_one, zero_add, Polynomial.derivative_sub,
       Polynomial.derivative_one, zero_sub, mul_neg, Nat.sub_zero, ← Nat.cast_succ,
-      Polynomial.c_eq_nat_cast]
+      Polynomial.C_eq_nat_cast]
   conv_rhs => rw [mul_sub]
   -- We'll prove the two terms match up separately.
   refine' congr (congr_arg Sub.sub _) _
@@ -315,7 +315,7 @@ theorem linearIndependent (n : ℕ) :
 
 theorem sum (n : ℕ) : (∑ ν in Finset.range (n + 1), bernsteinPolynomial R n ν) = 1 :=
   calc
-    (∑ ν in Finset.range (n + 1), bernsteinPolynomial R n ν) = (x + (1 - x)) ^ n :=
+    (∑ ν in Finset.range (n + 1), bernsteinPolynomial R n ν) = (X + (1 - X)) ^ n :=
       by
       rw [add_pow]
       simp only [bernsteinPolynomial, mul_comm, mul_assoc, mul_left_comm]
@@ -349,8 +349,8 @@ theorem sum_smul (n : ℕ) : (∑ ν in Finset.range (n + 1), ν • bernsteinPo
     have w :
       ∀ k : ℕ,
         k • bernsteinPolynomial R n k =
-          ↑k * Polynomial.x ^ (k - 1) * (1 - Polynomial.x) ^ (n - k) * ↑(n.choose k) *
-            Polynomial.x :=
+          ↑k * Polynomial.X ^ (k - 1) * (1 - Polynomial.X) ^ (n - k) * ↑(n.choose k) *
+            Polynomial.X :=
       by
       rintro (_ | k)
       · simp
@@ -396,8 +396,8 @@ theorem sum_mul_smul (n : ℕ) :
       ∀ k : ℕ,
         (k * (k - 1)) • bernsteinPolynomial R n k =
           ↑(n.choose k) *
-              ((1 - Polynomial.x) ^ (n - k) * (↑k * (↑(k - 1) * Polynomial.x ^ (k - 1 - 1)))) *
-            Polynomial.x ^ 2 :=
+              ((1 - Polynomial.X) ^ (n - k) * (↑k * (↑(k - 1) * Polynomial.X ^ (k - 1 - 1)))) *
+            Polynomial.X ^ 2 :=
       by
       rintro (_ | _ | k)
       · simp
@@ -426,12 +426,12 @@ theorem sum_mul_smul (n : ℕ) :
 which we'll want later.
 -/
 theorem variance (n : ℕ) :
-    (∑ ν in Finset.range (n + 1), (n • Polynomial.x - ν) ^ 2 * bernsteinPolynomial R n ν) =
-      n • Polynomial.x * (1 - Polynomial.x) :=
+    (∑ ν in Finset.range (n + 1), (n • Polynomial.X - ν) ^ 2 * bernsteinPolynomial R n ν) =
+      n • Polynomial.X * (1 - Polynomial.X) :=
   by
   have p :
     ((((Finset.range (n + 1)).Sum fun ν => (ν * (ν - 1)) • bernsteinPolynomial R n ν) +
-          (1 - (2 * n) • Polynomial.x) *
+          (1 - (2 * n) • Polynomial.X) *
             (Finset.range (n + 1)).Sum fun ν => ν • bernsteinPolynomial R n ν) +
         n ^ 2 • X ^ 2 * (Finset.range (n + 1)).Sum fun ν => bernsteinPolynomial R n ν) =
       _ :=

bbeb185d

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

bbeb185d

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

@@ -108,7 +108,7 @@ theorem derivative_succ_aux (n ν : ℕ) :
       (↑(n + 1) : R[X]) * ((n.choose ν : R[X]) * X ^ ν * (1 - X) ^ (n - ν) -
         (n.choose (ν + 1) : R[X]) * X ^ (ν + 1) * (1 - X) ^ (n - (ν + 1))) by
     simpa [Polynomial.derivative_pow, ← sub_eq_add_neg, Nat.succ_sub_succ_eq_sub,
-      Polynomial.derivative_mul, Polynomial.derivative_nat_cast, zero_mul,
+      Polynomial.derivative_mul, Polynomial.derivative_natCast, zero_mul,
       Nat.cast_add, algebraMap.coe_one, Polynomial.derivative_X, mul_one, zero_add,
       Polynomial.derivative_sub, Polynomial.derivative_one, zero_sub, mul_neg, Nat.sub_zero,
       bernsteinPolynomial, map_add, map_natCast, Nat.cast_one]
@@ -152,7 +152,7 @@ theorem iterate_derivative_at_0_eq_zero_of_lt (n : ℕ) {ν k : ℕ} :
     · simp [eval_at_0]
     · simp only [derivative_succ, Int.natCast_eq_zero, mul_eq_zero, Function.comp_apply,
         Function.iterate_succ, Polynomial.iterate_derivative_sub,
-        Polynomial.iterate_derivative_nat_cast_mul, Polynomial.eval_mul, Polynomial.eval_nat_cast,
+        Polynomial.iterate_derivative_natCast_mul, Polynomial.eval_mul, Polynomial.eval_natCast,
         Polynomial.eval_sub]
       intro h
       apply mul_eq_zero_of_right
@@ -179,8 +179,8 @@ theorem iterate_derivative_at_0 (n ν : ℕ) :
     · have h' : ν ≤ n - 1 := le_tsub_of_add_le_right h
       simp only [derivative_succ, ih (n - 1) h', iterate_derivative_succ_at_0_eq_zero,
         Nat.succ_sub_succ_eq_sub, tsub_zero, sub_zero, iterate_derivative_sub,
-        iterate_derivative_nat_cast_mul, eval_one, eval_mul, eval_add, eval_sub, eval_X, eval_comp,
-        eval_nat_cast, Function.comp_apply, Function.iterate_succ, ascPochhammer_succ_left]
+        iterate_derivative_natCast_mul, eval_one, eval_mul, eval_add, eval_sub, eval_X, eval_comp,
+        eval_natCast, Function.comp_apply, Function.iterate_succ, ascPochhammer_succ_left]
       obtain rfl | h'' := ν.eq_zero_or_pos
       · simp
       · have : n - 1 - (ν - 1) = n - ν := by
@@ -320,7 +320,7 @@ theorem sum_smul (n : ℕ) :
       rintro (_ | k)
       · simp
       · rw [bernsteinPolynomial]
-        simp only [← nat_cast_mul, Nat.succ_eq_add_one, Nat.add_succ_sub_one, add_zero, pow_succ]
+        simp only [← natCast_mul, Nat.succ_eq_add_one, Nat.add_succ_sub_one, add_zero, pow_succ]
         push_cast
         ring
     rw [add_pow, map_sum (pderiv true), map_sum (MvPolynomial.aeval e), Finset.sum_mul]
@@ -359,7 +359,7 @@ theorem sum_mul_smul (n : ℕ) :
       · simp
       · simp
       · rw [bernsteinPolynomial]
-        simp only [← nat_cast_mul, Nat.succ_eq_add_one, Nat.add_succ_sub_one, add_zero, pow_succ]
+        simp only [← natCast_mul, Nat.succ_eq_add_one, Nat.add_succ_sub_one, add_zero, pow_succ]
         push_cast
         ring
     rw [add_pow, map_sum (pderiv true), map_sum (pderiv true), map_sum (MvPolynomial.aeval e),
@@ -393,19 +393,19 @@ theorem variance (n : ℕ) :
   conv at p =>
     lhs
     rw [Finset.mul_sum, Finset.mul_sum, ← Finset.sum_add_distrib, ← Finset.sum_add_distrib]
-    simp only [← nat_cast_mul]
+    simp only [← natCast_mul]
     simp only [← mul_assoc]
     simp only [← add_mul]
   conv at p =>
     rhs
-    rw [sum, sum_smul, sum_mul_smul, ← nat_cast_mul]
+    rw [sum, sum_smul, sum_mul_smul, ← natCast_mul]
   calc
     _ = _ := Finset.sum_congr rfl fun k m => ?_
     _ = _ := p
     _ = _ := ?_
-  · congr 1; simp only [← nat_cast_mul, push_cast]
+  · congr 1; simp only [← natCast_mul, push_cast]
     cases k <;> · simp; ring
-  · simp only [← nat_cast_mul, push_cast]
+  · simp only [← natCast_mul, push_cast]
     cases n
     · simp
     · simp; ring

bbeb185d

chore: Rename coe_nat/coe_int/coe_rat to natCast/intCast/ratCast (#11499)

This is less exhaustive than its sibling #11486 because edge cases are harder to classify. No fundamental difficulty, just me being a bit fast and lazy.

Reduce the diff of #11203

b2af0d13

Diff

@@ -328,7 +328,7 @@ theorem sum_smul (n : ℕ) :
     refine' Finset.sum_congr rfl fun k _ => (w k).trans _
     simp only [x, y, e, pderiv_true_x, pderiv_true_y, Algebra.id.smul_eq_mul, nsmul_eq_mul,
       Bool.cond_true, Bool.cond_false, add_zero, mul_one, mul_zero, smul_zero, MvPolynomial.aeval_X,
-      MvPolynomial.pderiv_mul, Derivation.leibniz_pow, Derivation.map_coe_nat, map_natCast, map_pow,
+      MvPolynomial.pderiv_mul, Derivation.leibniz_pow, Derivation.map_natCast, map_natCast, map_pow,
       map_mul]
   · rw [(pderiv true).leibniz_pow, (pderiv true).map_add, pderiv_true_x, pderiv_true_y]
     simp only [x, y, e, Algebra.id.smul_eq_mul, nsmul_eq_mul, map_natCast, map_pow, map_add,
@@ -369,10 +369,10 @@ theorem sum_mul_smul (n : ℕ) :
     simp only [x, y, e, pderiv_true_x, pderiv_true_y, Algebra.id.smul_eq_mul, nsmul_eq_mul,
       Bool.cond_true, Bool.cond_false, add_zero, zero_add, mul_zero, smul_zero, mul_one,
       MvPolynomial.aeval_X, MvPolynomial.pderiv_X_self, MvPolynomial.pderiv_X_of_ne,
-      Derivation.leibniz_pow, Derivation.leibniz, Derivation.map_coe_nat, map_natCast, map_pow,
+      Derivation.leibniz_pow, Derivation.leibniz, Derivation.map_natCast, map_natCast, map_pow,
       map_mul, map_add]
   -- On the right hand side, we'll just simplify.
-  · simp only [x, y, e, pderiv_one, pderiv_mul, (pderiv _).leibniz_pow, (pderiv _).map_coe_nat,
+  · simp only [x, y, e, pderiv_one, pderiv_mul, (pderiv _).leibniz_pow, (pderiv _).map_natCast,
       (pderiv true).map_add, pderiv_true_x, pderiv_true_y, Algebra.id.smul_eq_mul, add_zero,
       mul_one, Derivation.map_smul_of_tower, map_nsmul, map_pow, map_add, Bool.cond_true,
       Bool.cond_false, MvPolynomial.aeval_X, add_sub_cancel, one_pow, smul_smul,

bbeb185d

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

@@ -3,12 +3,12 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathlib.Data.Polynomial.Derivative
+import Mathlib.Algebra.MvPolynomial.PDeriv
+import Mathlib.Algebra.Polynomial.AlgebraMap
+import Mathlib.Algebra.Polynomial.Derivative
 import Mathlib.Data.Nat.Choose.Sum
-import Mathlib.RingTheory.Polynomial.Pochhammer
-import Mathlib.Data.Polynomial.AlgebraMap
 import Mathlib.LinearAlgebra.LinearIndependent
-import Mathlib.Data.MvPolynomial.PDeriv
+import Mathlib.RingTheory.Polynomial.Pochhammer
 
 #align_import ring_theory.polynomial.bernstein from "leanprover-community/mathlib"@"bbeb185db4ccee8ed07dc48449414ebfa39cb821"

bbeb185d

chore(Data/Int): Rename coe_nat to natCast (#11637)

Reduce the diff of #11499

Renames

All in the Int namespace:

ofNat_eq_cast → ofNat_eq_natCast
cast_eq_cast_iff_Nat → natCast_inj
natCast_eq_ofNat → ofNat_eq_natCast
coe_nat_sub → natCast_sub
coe_nat_nonneg → natCast_nonneg
sign_coe_add_one → sign_natCast_add_one
nat_succ_eq_int_succ → natCast_succ
succ_neg_nat_succ → succ_neg_natCast_succ
coe_pred_of_pos → natCast_pred_of_pos
coe_nat_div → natCast_div
coe_nat_ediv → natCast_ediv
sign_coe_nat_of_nonzero → sign_natCast_of_ne_zero
toNat_coe_nat → toNat_natCast
toNat_coe_nat_add_one → toNat_natCast_add_one
coe_nat_dvd → natCast_dvd_natCast
coe_nat_dvd_left → natCast_dvd
coe_nat_dvd_right → dvd_natCast
le_coe_nat_sub → le_natCast_sub
succ_coe_nat_pos → succ_natCast_pos
coe_nat_modEq_iff → natCast_modEq_iff
coe_natAbs → natCast_natAbs
coe_nat_eq_zero → natCast_eq_zero
coe_nat_ne_zero → natCast_ne_zero
coe_nat_ne_zero_iff_pos → natCast_ne_zero_iff_pos
abs_coe_nat → abs_natCast
coe_nat_nonpos_iff → natCast_nonpos_iff

Also rename Nat.coe_nat_dvd to Nat.cast_dvd_cast

392a24a9

Diff

@@ -150,7 +150,7 @@ theorem iterate_derivative_at_0_eq_zero_of_lt (n : ℕ) {ν k : ℕ} :
   · rw [Nat.lt_succ_iff]
     induction' k with k ih generalizing n ν
     · simp [eval_at_0]
-    · simp only [derivative_succ, Int.coe_nat_eq_zero, mul_eq_zero, Function.comp_apply,
+    · simp only [derivative_succ, Int.natCast_eq_zero, mul_eq_zero, Function.comp_apply,
         Function.iterate_succ, Polynomial.iterate_derivative_sub,
         Polynomial.iterate_derivative_nat_cast_mul, Polynomial.eval_mul, Polynomial.eval_nat_cast,
         Polynomial.eval_sub]
@@ -195,8 +195,7 @@ theorem iterate_derivative_at_0 (n ν : ℕ) :
 
 theorem iterate_derivative_at_0_ne_zero [CharZero R] (n ν : ℕ) (h : ν ≤ n) :
     (Polynomial.derivative^[ν] (bernsteinPolynomial R n ν)).eval 0 ≠ 0 := by
-  simp only [Int.coe_nat_eq_zero, bernsteinPolynomial.iterate_derivative_at_0, Ne,
-    Nat.cast_eq_zero]
+  simp only [Int.natCast_eq_zero, bernsteinPolynomial.iterate_derivative_at_0, Ne, Nat.cast_eq_zero]
   simp only [← ascPochhammer_eval_cast]
   norm_cast
   apply ne_of_gt

bbeb185d

chore(RingTheory): delete useless lemma (#11827)

As discussed in https://github.com/leanprover-community/mathlib4/pull/11790 for the case of Lie derivations, it seems that this map_sum lemma is not useful since we can use the generic version.

a2b6e2ea

Diff

@@ -324,7 +324,7 @@ theorem sum_smul (n : ℕ) :
         simp only [← nat_cast_mul, Nat.succ_eq_add_one, Nat.add_succ_sub_one, add_zero, pow_succ]
         push_cast
         ring
-    rw [add_pow, (pderiv true).map_sum, (MvPolynomial.aeval e).map_sum, Finset.sum_mul]
+    rw [add_pow, map_sum (pderiv true), map_sum (MvPolynomial.aeval e), Finset.sum_mul]
     -- Step inside the sum:
     refine' Finset.sum_congr rfl fun k _ => (w k).trans _
     simp only [x, y, e, pderiv_true_x, pderiv_true_y, Algebra.id.smul_eq_mul, nsmul_eq_mul,
@@ -363,7 +363,7 @@ theorem sum_mul_smul (n : ℕ) :
         simp only [← nat_cast_mul, Nat.succ_eq_add_one, Nat.add_succ_sub_one, add_zero, pow_succ]
         push_cast
         ring
-    rw [add_pow, (pderiv true).map_sum, (pderiv true).map_sum, (MvPolynomial.aeval e).map_sum,
+    rw [add_pow, map_sum (pderiv true), map_sum (pderiv true), map_sum (MvPolynomial.aeval e),
       Finset.sum_mul]
     -- Step inside the sum:
     refine' Finset.sum_congr rfl fun k _ => (w k).trans _

bbeb185d

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11813)

08686b25

Diff

@@ -195,7 +195,7 @@ theorem iterate_derivative_at_0 (n ν : ℕ) :
 
 theorem iterate_derivative_at_0_ne_zero [CharZero R] (n ν : ℕ) (h : ν ≤ n) :
     (Polynomial.derivative^[ν] (bernsteinPolynomial R n ν)).eval 0 ≠ 0 := by
-  simp only [Int.coe_nat_eq_zero, bernsteinPolynomial.iterate_derivative_at_0, Ne.def,
+  simp only [Int.coe_nat_eq_zero, bernsteinPolynomial.iterate_derivative_at_0, Ne,
     Nat.cast_eq_zero]
   simp only [← ascPochhammer_eval_cast]
   norm_cast
@@ -234,7 +234,7 @@ theorem iterate_derivative_at_1 (n ν : ℕ) (h : ν ≤ n) :
 
 theorem iterate_derivative_at_1_ne_zero [CharZero R] (n ν : ℕ) (h : ν ≤ n) :
     (Polynomial.derivative^[n - ν] (bernsteinPolynomial R n ν)).eval 1 ≠ 0 := by
-  rw [bernsteinPolynomial.iterate_derivative_at_1 _ _ _ h, Ne.def, neg_one_pow_mul_eq_zero_iff, ←
+  rw [bernsteinPolynomial.iterate_derivative_at_1 _ _ _ h, Ne, neg_one_pow_mul_eq_zero_iff, ←
     Nat.cast_succ, ← ascPochhammer_eval_cast, ← Nat.cast_zero, Nat.cast_inj]
   exact (ascPochhammer_pos _ _ (Nat.succ_pos ν)).ne'
 #align bernstein_polynomial.iterate_derivative_at_1_ne_zero bernsteinPolynomial.iterate_derivative_at_1_ne_zero

bbeb185d

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

@@ -333,7 +333,7 @@ theorem sum_smul (n : ℕ) :
       map_mul]
   · rw [(pderiv true).leibniz_pow, (pderiv true).map_add, pderiv_true_x, pderiv_true_y]
     simp only [x, y, e, Algebra.id.smul_eq_mul, nsmul_eq_mul, map_natCast, map_pow, map_add,
-      map_mul, Bool.cond_true, Bool.cond_false, MvPolynomial.aeval_X, add_sub_cancel'_right,
+      map_mul, Bool.cond_true, Bool.cond_false, MvPolynomial.aeval_X, add_sub_cancel,
       one_pow, add_zero, mul_one]
 #align bernstein_polynomial.sum_smul bernsteinPolynomial.sum_smul
 
@@ -376,7 +376,7 @@ theorem sum_mul_smul (n : ℕ) :
   · simp only [x, y, e, pderiv_one, pderiv_mul, (pderiv _).leibniz_pow, (pderiv _).map_coe_nat,
       (pderiv true).map_add, pderiv_true_x, pderiv_true_y, Algebra.id.smul_eq_mul, add_zero,
       mul_one, Derivation.map_smul_of_tower, map_nsmul, map_pow, map_add, Bool.cond_true,
-      Bool.cond_false, MvPolynomial.aeval_X, add_sub_cancel'_right, one_pow, smul_smul,
+      Bool.cond_false, MvPolynomial.aeval_X, add_sub_cancel, one_pow, smul_smul,
       smul_one_mul]
 #align bernstein_polynomial.sum_mul_smul bernsteinPolynomial.sum_mul_smul

bbeb185d

chore: golf using omega (#11318)

Backported from #11314.

bbf22060

Diff

@@ -227,9 +227,9 @@ theorem iterate_derivative_at_1 (n ν : ℕ) (h : ν ≤ n) :
   simp [Polynomial.eval_comp, h]
   obtain rfl | h' := h.eq_or_lt
   · simp
-  · congr
-    norm_cast
-    rw [← tsub_add_eq_tsub_tsub, tsub_tsub_cancel_of_le (Nat.succ_le_iff.mpr h')]
+  · norm_cast
+    congr
+    omega
 #align bernstein_polynomial.iterate_derivative_at_1 bernsteinPolynomial.iterate_derivative_at_1
 
 theorem iterate_derivative_at_1_ne_zero [CharZero R] (n ν : ℕ) (h : ν ≤ n) :

bbeb185d

chore: more backporting of simp changes from #10995 (#11001)

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

d9589c14

Diff

@@ -327,14 +327,14 @@ theorem sum_smul (n : ℕ) :
     rw [add_pow, (pderiv true).map_sum, (MvPolynomial.aeval e).map_sum, Finset.sum_mul]
     -- Step inside the sum:
     refine' Finset.sum_congr rfl fun k _ => (w k).trans _
-    simp only [pderiv_true_x, pderiv_true_y, Algebra.id.smul_eq_mul, nsmul_eq_mul, Bool.cond_true,
-      Bool.cond_false, add_zero, mul_one, mul_zero, smul_zero, MvPolynomial.aeval_X,
+    simp only [x, y, e, pderiv_true_x, pderiv_true_y, Algebra.id.smul_eq_mul, nsmul_eq_mul,
+      Bool.cond_true, Bool.cond_false, add_zero, mul_one, mul_zero, smul_zero, MvPolynomial.aeval_X,
       MvPolynomial.pderiv_mul, Derivation.leibniz_pow, Derivation.map_coe_nat, map_natCast, map_pow,
       map_mul]
   · rw [(pderiv true).leibniz_pow, (pderiv true).map_add, pderiv_true_x, pderiv_true_y]
-    simp only [Algebra.id.smul_eq_mul, nsmul_eq_mul, map_natCast, map_pow, map_add, map_mul,
-      Bool.cond_true, Bool.cond_false, MvPolynomial.aeval_X, add_sub_cancel'_right, one_pow,
-      add_zero, mul_one]
+    simp only [x, y, e, Algebra.id.smul_eq_mul, nsmul_eq_mul, map_natCast, map_pow, map_add,
+      map_mul, Bool.cond_true, Bool.cond_false, MvPolynomial.aeval_X, add_sub_cancel'_right,
+      one_pow, add_zero, mul_one]
 #align bernstein_polynomial.sum_smul bernsteinPolynomial.sum_smul
 
 theorem sum_mul_smul (n : ℕ) :
@@ -367,13 +367,13 @@ theorem sum_mul_smul (n : ℕ) :
       Finset.sum_mul]
     -- Step inside the sum:
     refine' Finset.sum_congr rfl fun k _ => (w k).trans _
-    simp only [pderiv_true_x, pderiv_true_y, Algebra.id.smul_eq_mul, nsmul_eq_mul, Bool.cond_true,
-      Bool.cond_false, add_zero, zero_add, mul_zero, smul_zero, mul_one,
+    simp only [x, y, e, pderiv_true_x, pderiv_true_y, Algebra.id.smul_eq_mul, nsmul_eq_mul,
+      Bool.cond_true, Bool.cond_false, add_zero, zero_add, mul_zero, smul_zero, mul_one,
       MvPolynomial.aeval_X, MvPolynomial.pderiv_X_self, MvPolynomial.pderiv_X_of_ne,
       Derivation.leibniz_pow, Derivation.leibniz, Derivation.map_coe_nat, map_natCast, map_pow,
       map_mul, map_add]
   -- On the right hand side, we'll just simplify.
-  · simp only [pderiv_one, pderiv_mul, (pderiv _).leibniz_pow, (pderiv _).map_coe_nat,
+  · simp only [x, y, e, pderiv_one, pderiv_mul, (pderiv _).leibniz_pow, (pderiv _).map_coe_nat,
       (pderiv true).map_add, pderiv_true_x, pderiv_true_y, Algebra.id.smul_eq_mul, add_zero,
       mul_one, Derivation.map_smul_of_tower, map_nsmul, map_pow, map_add, Bool.cond_true,
       Bool.cond_false, MvPolynomial.aeval_X, add_sub_cancel'_right, one_pow, smul_smul,

bbeb185d

refactor(Data/FunLike): use unbundled inheritance from FunLike (#8386)

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

`simp` not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

c6a73d4f

Diff

@@ -257,7 +257,8 @@ theorem linearIndependent_aux (n k : ℕ) (h : k ≤ n + 1) :
       simp only [Fin.val_last, Fin.init_def]
       dsimp
       apply not_mem_span_of_apply_not_mem_span_image (@Polynomial.derivative ℚ _ ^ (n - k))
-      simp only [not_exists, not_and, Submodule.mem_map, Submodule.span_image]
+      -- Note: #8386 had to change `span_image` into `span_image _`
+      simp only [not_exists, not_and, Submodule.mem_map, Submodule.span_image _]
       intro p m
       apply_fun Polynomial.eval (1 : ℚ)
       simp only [LinearMap.pow_apply]

bbeb185d

feat: The support of f ^ n (#9617)

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

From LeanAPAP

9d1a7d26

Diff

@@ -87,16 +87,16 @@ theorem eval_at_0 (n ν : ℕ) : (bernsteinPolynomial R n ν).eval 0 = if ν = 0
   rw [bernsteinPolynomial]
   split_ifs with h
   · subst h; simp
-  · simp [zero_pow (Nat.pos_of_ne_zero h)]
+  · simp [zero_pow h]
 #align bernstein_polynomial.eval_at_0 bernsteinPolynomial.eval_at_0
 
 theorem eval_at_1 (n ν : ℕ) : (bernsteinPolynomial R n ν).eval 1 = if ν = n then 1 else 0 := by
   rw [bernsteinPolynomial]
   split_ifs with h
   · subst h; simp
-  · obtain w | w := (n - ν).eq_zero_or_pos
-    · simp [Nat.choose_eq_zero_of_lt ((tsub_eq_zero_iff_le.mp w).lt_of_ne (Ne.symm h))]
-    · simp [zero_pow w]
+  · obtain hνn | hnν := Ne.lt_or_lt h
+    · simp [zero_pow $ Nat.sub_ne_zero_of_lt hνn]
+    · simp [Nat.choose_eq_zero_of_lt hnν]
 #align bernstein_polynomial.eval_at_1 bernsteinPolynomial.eval_at_1
 
 theorem derivative_succ_aux (n ν : ℕ) :

bbeb185d

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

@@ -118,7 +118,7 @@ theorem derivative_succ_aux (n ν : ℕ) :
   · simp only [← mul_assoc]
     refine' congr (congr_arg (· * ·) (congr (congr_arg (· * ·) _) rfl)) rfl
     -- Now it's just about binomial coefficients
-    exact_mod_cast congr_arg (fun m : ℕ => (m : R[X])) (Nat.succ_mul_choose_eq n ν).symm
+    exact mod_cast congr_arg (fun m : ℕ => (m : R[X])) (Nat.succ_mul_choose_eq n ν).symm
   · rw [← tsub_add_eq_tsub_tsub, ← mul_assoc, ← mul_assoc]; congr 1
     rw [mul_comm, ← mul_assoc, ← mul_assoc]; congr 1
     norm_cast

bbeb185d

fix: patch for std4#195 (more succ/pred lemmas for Nat) (#6203)

cdcad962

Diff

@@ -189,7 +189,7 @@ theorem iterate_derivative_at_0 (n ν : ℕ) :
         rw [this, ascPochhammer_eval_succ]
         rw_mod_cast [tsub_add_cancel_of_le (h'.trans n.pred_le)]
   · simp only [not_le] at h
-    rw [tsub_eq_zero_iff_le.mpr (Nat.le_pred_of_lt h), eq_zero_of_lt R h]
+    rw [tsub_eq_zero_iff_le.mpr (Nat.le_sub_one_of_lt h), eq_zero_of_lt R h]
     simp [pos_iff_ne_zero.mp (pos_of_gt h)]
 #align bernstein_polynomial.iterate_derivative_at_0 bernsteinPolynomial.iterate_derivative_at_0

bbeb185d

chore: rename pochhammer (#6917)

We rename pochhammer to ascPochhammer to prepare adding descPochhammer.

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

ae1eb5e7

Diff

@@ -172,7 +172,7 @@ open Polynomial
 @[simp]
 theorem iterate_derivative_at_0 (n ν : ℕ) :
     (Polynomial.derivative^[ν] (bernsteinPolynomial R n ν)).eval 0 =
-      (pochhammer R ν).eval ((n - (ν - 1) : ℕ) : R) := by
+      (ascPochhammer R ν).eval ((n - (ν - 1) : ℕ) : R) := by
   by_cases h : ν ≤ n
   · induction' ν with ν ih generalizing n
     · simp [eval_at_0]
@@ -180,13 +180,13 @@ theorem iterate_derivative_at_0 (n ν : ℕ) :
       simp only [derivative_succ, ih (n - 1) h', iterate_derivative_succ_at_0_eq_zero,
         Nat.succ_sub_succ_eq_sub, tsub_zero, sub_zero, iterate_derivative_sub,
         iterate_derivative_nat_cast_mul, eval_one, eval_mul, eval_add, eval_sub, eval_X, eval_comp,
-        eval_nat_cast, Function.comp_apply, Function.iterate_succ, pochhammer_succ_left]
+        eval_nat_cast, Function.comp_apply, Function.iterate_succ, ascPochhammer_succ_left]
       obtain rfl | h'' := ν.eq_zero_or_pos
       · simp
       · have : n - 1 - (ν - 1) = n - ν := by
           rw [gt_iff_lt, ← Nat.succ_le_iff] at h''
           rw [← tsub_add_eq_tsub_tsub, add_comm, tsub_add_cancel_of_le h'']
-        rw [this, pochhammer_eval_succ]
+        rw [this, ascPochhammer_eval_succ]
         rw_mod_cast [tsub_add_cancel_of_le (h'.trans n.pred_le)]
   · simp only [not_le] at h
     rw [tsub_eq_zero_iff_le.mpr (Nat.le_pred_of_lt h), eq_zero_of_lt R h]
@@ -197,13 +197,13 @@ theorem iterate_derivative_at_0_ne_zero [CharZero R] (n ν : ℕ) (h : ν ≤ n)
     (Polynomial.derivative^[ν] (bernsteinPolynomial R n ν)).eval 0 ≠ 0 := by
   simp only [Int.coe_nat_eq_zero, bernsteinPolynomial.iterate_derivative_at_0, Ne.def,
     Nat.cast_eq_zero]
-  simp only [← pochhammer_eval_cast]
+  simp only [← ascPochhammer_eval_cast]
   norm_cast
   apply ne_of_gt
   obtain rfl | h' := Nat.eq_zero_or_pos ν
   · simp
   · rw [← Nat.succ_pred_eq_of_pos h'] at h
-    exact pochhammer_pos _ _ (tsub_pos_of_lt (Nat.lt_of_succ_le h))
+    exact ascPochhammer_pos _ _ (tsub_pos_of_lt (Nat.lt_of_succ_le h))
 #align bernstein_polynomial.iterate_derivative_at_0_ne_zero bernsteinPolynomial.iterate_derivative_at_0_ne_zero
 
 /-!
@@ -222,7 +222,7 @@ theorem iterate_derivative_at_1_eq_zero_of_lt (n : ℕ) {ν k : ℕ} :
 @[simp]
 theorem iterate_derivative_at_1 (n ν : ℕ) (h : ν ≤ n) :
     (Polynomial.derivative^[n - ν] (bernsteinPolynomial R n ν)).eval 1 =
-      (-1) ^ (n - ν) * (pochhammer R (n - ν)).eval (ν + 1 : R) := by
+      (-1) ^ (n - ν) * (ascPochhammer R (n - ν)).eval (ν + 1 : R) := by
   rw [flip' _ _ _ h]
   simp [Polynomial.eval_comp, h]
   obtain rfl | h' := h.eq_or_lt
@@ -235,8 +235,8 @@ theorem iterate_derivative_at_1 (n ν : ℕ) (h : ν ≤ n) :
 theorem iterate_derivative_at_1_ne_zero [CharZero R] (n ν : ℕ) (h : ν ≤ n) :
     (Polynomial.derivative^[n - ν] (bernsteinPolynomial R n ν)).eval 1 ≠ 0 := by
   rw [bernsteinPolynomial.iterate_derivative_at_1 _ _ _ h, Ne.def, neg_one_pow_mul_eq_zero_iff, ←
-    Nat.cast_succ, ← pochhammer_eval_cast, ← Nat.cast_zero, Nat.cast_inj]
-  exact (pochhammer_pos _ _ (Nat.succ_pos ν)).ne'
+    Nat.cast_succ, ← ascPochhammer_eval_cast, ← Nat.cast_zero, Nat.cast_inj]
+  exact (ascPochhammer_pos _ _ (Nat.succ_pos ν)).ne'
 #align bernstein_polynomial.iterate_derivative_at_1_ne_zero bernsteinPolynomial.iterate_derivative_at_1_ne_zero
 
 open Submodule

bbeb185d

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

@@ -53,10 +53,7 @@ def bernsteinPolynomial (n ν : ℕ) : R[X] :=
 #align bernstein_polynomial bernsteinPolynomial
 
 example : bernsteinPolynomial ℤ 3 2 = 3 * X ^ 2 - 3 * X ^ 3 := by
-  -- Porting note: Originally was just `norm_num [bernsteinPolynomial, choose]; ring`,
-  -- but `norm_num` ignores arguments
-  simp [bernsteinPolynomial, choose]
-  norm_num
+  norm_num [bernsteinPolynomial, choose]
   ring
 
 namespace bernsteinPolynomial

bbeb185d

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

@@ -111,7 +111,7 @@ theorem derivative_succ_aux (n ν : ℕ) :
       (↑(n + 1) : R[X]) * ((n.choose ν : R[X]) * X ^ ν * (1 - X) ^ (n - ν) -
         (n.choose (ν + 1) : R[X]) * X ^ (ν + 1) * (1 - X) ^ (n - (ν + 1))) by
     simpa [Polynomial.derivative_pow, ← sub_eq_add_neg, Nat.succ_sub_succ_eq_sub,
-      Polynomial.derivative_mul, Polynomial.derivative_nat_cast, MulZeroClass.zero_mul,
+      Polynomial.derivative_mul, Polynomial.derivative_nat_cast, zero_mul,
       Nat.cast_add, algebraMap.coe_one, Polynomial.derivative_X, mul_one, zero_add,
       Polynomial.derivative_sub, Polynomial.derivative_one, zero_sub, mul_neg, Nat.sub_zero,
       bernsteinPolynomial, map_add, map_natCast, Nat.cast_one]
@@ -330,7 +330,7 @@ theorem sum_smul (n : ℕ) :
     -- Step inside the sum:
     refine' Finset.sum_congr rfl fun k _ => (w k).trans _
     simp only [pderiv_true_x, pderiv_true_y, Algebra.id.smul_eq_mul, nsmul_eq_mul, Bool.cond_true,
-      Bool.cond_false, add_zero, mul_one, MulZeroClass.mul_zero, smul_zero, MvPolynomial.aeval_X,
+      Bool.cond_false, add_zero, mul_one, mul_zero, smul_zero, MvPolynomial.aeval_X,
       MvPolynomial.pderiv_mul, Derivation.leibniz_pow, Derivation.map_coe_nat, map_natCast, map_pow,
       map_mul]
   · rw [(pderiv true).leibniz_pow, (pderiv true).map_add, pderiv_true_x, pderiv_true_y]
@@ -370,7 +370,7 @@ theorem sum_mul_smul (n : ℕ) :
     -- Step inside the sum:
     refine' Finset.sum_congr rfl fun k _ => (w k).trans _
     simp only [pderiv_true_x, pderiv_true_y, Algebra.id.smul_eq_mul, nsmul_eq_mul, Bool.cond_true,
-      Bool.cond_false, add_zero, zero_add, MulZeroClass.mul_zero, smul_zero, mul_one,
+      Bool.cond_false, add_zero, zero_add, mul_zero, smul_zero, mul_one,
       MvPolynomial.aeval_X, MvPolynomial.pderiv_X_self, MvPolynomial.pderiv_X_of_ne,
       Derivation.leibniz_pow, Derivation.leibniz, Derivation.map_coe_nat, map_natCast, map_pow,
       map_mul, map_add]

bbeb185d

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

@@ -17,7 +17,7 @@ import Mathlib.Data.MvPolynomial.PDeriv
 
 The definition of the Bernstein polynomials
 ```
-bernsteinPolynomial (R : Type _) [CommRing R] (n ν : ℕ) : R[X] :=
+bernsteinPolynomial (R : Type*) [CommRing R] (n ν : ℕ) : R[X] :=
 (choose n ν) * X^ν * (1 - X)^(n - ν)
 ```
 and the fact that for `ν : fin (n+1)` these are linearly independent over `ℚ`.
@@ -42,7 +42,7 @@ open Polynomial (X)
 
 open scoped BigOperators Polynomial
 
-variable (R : Type _) [CommRing R]
+variable (R : Type*) [CommRing R]
 
 /-- `bernsteinPolynomial R n ν` is `(choose n ν) * X^ν * (1 - X)^(n - ν)`.
 
@@ -67,7 +67,7 @@ theorem eq_zero_of_lt {n ν : ℕ} (h : n < ν) : bernsteinPolynomial R n ν = 0
 
 section
 
-variable {R} {S : Type _} [CommRing S]
+variable {R} {S : Type*} [CommRing S]
 
 @[simp]
 theorem map (f : R →+* S) (n ν : ℕ) :

bbeb185d

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module ring_theory.polynomial.bernstein
-! leanprover-community/mathlib commit bbeb185db4ccee8ed07dc48449414ebfa39cb821
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Polynomial.Derivative
 import Mathlib.Data.Nat.Choose.Sum
@@ -15,6 +10,8 @@ import Mathlib.Data.Polynomial.AlgebraMap
 import Mathlib.LinearAlgebra.LinearIndependent
 import Mathlib.Data.MvPolynomial.PDeriv
 
+#align_import ring_theory.polynomial.bernstein from "leanprover-community/mathlib"@"bbeb185db4ccee8ed07dc48449414ebfa39cb821"
+
 /-!
 # Bernstein polynomials

bbeb185d

fix precedence of Nat.iterate (#5589)

bd2fff86

Diff

@@ -150,7 +150,7 @@ theorem derivative_zero (n : ℕ) :
 #align bernstein_polynomial.derivative_zero bernsteinPolynomial.derivative_zero
 
 theorem iterate_derivative_at_0_eq_zero_of_lt (n : ℕ) {ν k : ℕ} :
-    k < ν → ((Polynomial.derivative^[k]) (bernsteinPolynomial R n ν)).eval 0 = 0 := by
+    k < ν → (Polynomial.derivative^[k] (bernsteinPolynomial R n ν)).eval 0 = 0 := by
   cases' ν with ν
   · rintro ⟨⟩
   · rw [Nat.lt_succ_iff]
@@ -169,7 +169,7 @@ theorem iterate_derivative_at_0_eq_zero_of_lt (n : ℕ) {ν k : ℕ} :
 
 @[simp]
 theorem iterate_derivative_succ_at_0_eq_zero (n ν : ℕ) :
-    ((Polynomial.derivative^[ν]) (bernsteinPolynomial R n (ν + 1))).eval 0 = 0 :=
+    (Polynomial.derivative^[ν] (bernsteinPolynomial R n (ν + 1))).eval 0 = 0 :=
   iterate_derivative_at_0_eq_zero_of_lt R n (lt_add_one ν)
 #align bernstein_polynomial.iterate_derivative_succ_at_0_eq_zero bernsteinPolynomial.iterate_derivative_succ_at_0_eq_zero
 
@@ -177,7 +177,7 @@ open Polynomial
 
 @[simp]
 theorem iterate_derivative_at_0 (n ν : ℕ) :
-    ((Polynomial.derivative^[ν]) (bernsteinPolynomial R n ν)).eval 0 =
+    (Polynomial.derivative^[ν] (bernsteinPolynomial R n ν)).eval 0 =
       (pochhammer R ν).eval ((n - (ν - 1) : ℕ) : R) := by
   by_cases h : ν ≤ n
   · induction' ν with ν ih generalizing n
@@ -200,7 +200,7 @@ theorem iterate_derivative_at_0 (n ν : ℕ) :
 #align bernstein_polynomial.iterate_derivative_at_0 bernsteinPolynomial.iterate_derivative_at_0
 
 theorem iterate_derivative_at_0_ne_zero [CharZero R] (n ν : ℕ) (h : ν ≤ n) :
-    ((Polynomial.derivative^[ν]) (bernsteinPolynomial R n ν)).eval 0 ≠ 0 := by
+    (Polynomial.derivative^[ν] (bernsteinPolynomial R n ν)).eval 0 ≠ 0 := by
   simp only [Int.coe_nat_eq_zero, bernsteinPolynomial.iterate_derivative_at_0, Ne.def,
     Nat.cast_eq_zero]
   simp only [← pochhammer_eval_cast]
@@ -219,7 +219,7 @@ we use the symmetry of the Bernstein polynomials.
 
 
 theorem iterate_derivative_at_1_eq_zero_of_lt (n : ℕ) {ν k : ℕ} :
-    k < n - ν → ((Polynomial.derivative^[k]) (bernsteinPolynomial R n ν)).eval 1 = 0 := by
+    k < n - ν → (Polynomial.derivative^[k] (bernsteinPolynomial R n ν)).eval 1 = 0 := by
   intro w
   rw [flip' _ _ _ (tsub_pos_iff_lt.mp (pos_of_gt w)).le]
   simp [Polynomial.eval_comp, iterate_derivative_at_0_eq_zero_of_lt R n w]
@@ -227,7 +227,7 @@ theorem iterate_derivative_at_1_eq_zero_of_lt (n : ℕ) {ν k : ℕ} :
 
 @[simp]
 theorem iterate_derivative_at_1 (n ν : ℕ) (h : ν ≤ n) :
-    ((Polynomial.derivative^[n - ν]) (bernsteinPolynomial R n ν)).eval 1 =
+    (Polynomial.derivative^[n - ν] (bernsteinPolynomial R n ν)).eval 1 =
       (-1) ^ (n - ν) * (pochhammer R (n - ν)).eval (ν + 1 : R) := by
   rw [flip' _ _ _ h]
   simp [Polynomial.eval_comp, h]
@@ -239,7 +239,7 @@ theorem iterate_derivative_at_1 (n ν : ℕ) (h : ν ≤ n) :
 #align bernstein_polynomial.iterate_derivative_at_1 bernsteinPolynomial.iterate_derivative_at_1
 
 theorem iterate_derivative_at_1_ne_zero [CharZero R] (n ν : ℕ) (h : ν ≤ n) :
-    ((Polynomial.derivative^[n - ν]) (bernsteinPolynomial R n ν)).eval 1 ≠ 0 := by
+    (Polynomial.derivative^[n - ν] (bernsteinPolynomial R n ν)).eval 1 ≠ 0 := by
   rw [bernsteinPolynomial.iterate_derivative_at_1 _ _ _ h, Ne.def, neg_one_pow_mul_eq_zero_iff, ←
     Nat.cast_succ, ← pochhammer_eval_cast, ← Nat.cast_zero, Nat.cast_inj]
   exact (pochhammer_pos _ _ (Nat.succ_pos ν)).ne'
@@ -269,7 +269,7 @@ theorem linearIndependent_aux (n k : ℕ) (h : k ≤ n + 1) :
       simp only [LinearMap.pow_apply]
       -- The right hand side is nonzero,
       -- so it will suffice to show the left hand side is always zero.
-      suffices ((Polynomial.derivative^[n - k]) p).eval 1 = 0 by
+      suffices (Polynomial.derivative^[n - k] p).eval 1 = 0 by
         rw [this]
         exact (iterate_derivative_at_1_ne_zero ℚ n k h).symm
       refine span_induction m ?_ ?_ ?_ ?_

bbeb185d

chore: clean up spacing around at and goals (#5387)

Changes are of the form

some_tactic at h⊢ -> some_tactic at h ⊢
some_tactic at h -> some_tactic at h

2a870323

Diff

@@ -20,7 +20,7 @@ import Mathlib.Data.MvPolynomial.PDeriv
 
 The definition of the Bernstein polynomials
 ```
-bernsteinPolynomial (R : Type*) [comm_ring R] (n ν : ℕ) : R[X] :=
+bernsteinPolynomial (R : Type _) [CommRing R] (n ν : ℕ) : R[X] :=
 (choose n ν) * X^ν * (1 - X)^(n - ν)
 ```
 and the fact that for `ν : fin (n+1)` these are linearly independent over `ℚ`.

bbeb185d

chore: convert lambda in docs to fun (#5045)

Found with git grep -n "λ [a-zA-Z_ ]*,"

1164cf04

Diff

@@ -26,9 +26,9 @@ bernsteinPolynomial (R : Type*) [comm_ring R] (n ν : ℕ) : R[X] :=
 and the fact that for `ν : fin (n+1)` these are linearly independent over `ℚ`.
 
 We prove the basic identities
-* `(Finset.range (n + 1)).sum (λ ν, bernsteinPolynomial R n ν) = 1`
-* `(Finset.range (n + 1)).sum (λ ν, ν • bernsteinPolynomial R n ν) = n • X`
-* `(Finset.range (n + 1)).sum (λ ν, (ν * (ν-1)) • bernsteinPolynomial R n ν) = (n * (n-1)) • X^2`
+* `(Finset.range (n + 1)).sum (fun ν ↦ bernsteinPolynomial R n ν) = 1`
+* `(Finset.range (n + 1)).sum (fun ν ↦ ν • bernsteinPolynomial R n ν) = n • X`
+* `(Finset.range (n + 1)).sum (fun ν ↦ (ν * (ν-1)) • bernsteinPolynomial R n ν) = (n * (n-1)) • X^2`
 
 ## Notes

bbeb185d

feat: port RingTheory.Polynomial.Bernstein (#4661)

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

fb8ee975

`ring_theory.polynomial.bernstein` ⟷ `Mathlib.RingTheory.Polynomial.Bernstein`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Important changes

Remaining issues

Slower (failing) search

`simp` not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 8 + 481

ring_theory.polynomial.bernstein ⟷ Mathlib.RingTheory.Polynomial.Bernstein

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Important changes

Remaining issues

Slower (failing) search

simp not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 8 + 481

`ring_theory.polynomial.bernstein` ⟷ `Mathlib.RingTheory.Polynomial.Bernstein`

`simp` not firing sometimes