wiedijk_100_theorems.solution_of_cubic ⟷ Archive.Wiedijk100Theorems.SolutionOfCubic

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

@@ -147,7 +147,7 @@ theorem cubic_eq_zero_iff_of_p_eq_zero (ha : a ≠ 0) (hω : IsPrimitiveRoot ω
   have hi3 : (3 : K) ≠ 0 := nonzero_of_invertible _
   have h54 : (54 : K) = 2 * 3 ^ 3 := by norm_num
   have hb2 : b ^ 2 = 3 * a * c := by rw [sub_eq_zero] at hpz; rw [hpz]
-  have hb3 : b ^ 3 = 3 * a * b * c := by rw [pow_succ, hb2]; ring
+  have hb3 : b ^ 3 = 3 * a * b * c := by rw [pow_succ', hb2]; ring
   have h₂ :=
     calc
       a * x ^ 3 + b * x ^ 2 + c * x + d =

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

@@ -146,7 +146,7 @@ theorem cubic_eq_zero_iff_of_p_eq_zero (ha : a ≠ 0) (hω : IsPrimitiveRoot ω
   have hi2 : (2 : K) ≠ 0 := nonzero_of_invertible _
   have hi3 : (3 : K) ≠ 0 := nonzero_of_invertible _
   have h54 : (54 : K) = 2 * 3 ^ 3 := by norm_num
-  have hb2 : b ^ 2 = 3 * a * c := by rw [sub_eq_zero] at hpz ; rw [hpz]
+  have hb2 : b ^ 2 = 3 * a * c := by rw [sub_eq_zero] at hpz; rw [hpz]
   have hb3 : b ^ 3 = 3 * a * b * c := by rw [pow_succ, hb2]; ring
   have h₂ :=
     calc

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Jeoff Lee. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeoff Lee
 -/
-import Mathbin.Tactic.LinearCombination
-import Mathbin.RingTheory.Polynomial.Cyclotomic.Roots
+import Tactic.LinearCombination
+import RingTheory.Polynomial.Cyclotomic.Roots
 
 #align_import wiedijk_100_theorems.solution_of_cubic from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Jeoff Lee. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeoff Lee
-
-! This file was ported from Lean 3 source module wiedijk_100_theorems.solution_of_cubic
-! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Tactic.LinearCombination
 import Mathbin.RingTheory.Polynomial.Cyclotomic.Roots
 
+#align_import wiedijk_100_theorems.solution_of_cubic from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
+
 /-!
 # The Solution of a Cubic
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/bf2428c9486c407ca38b5b3fb10b87dad0bc99fa

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeoff Lee
 
 ! This file was ported from Lean 3 source module wiedijk_100_theorems.solution_of_cubic
-! leanprover-community/mathlib commit 5563b1b49e86e135e8c7b556da5ad2f5ff881cad
+! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.Polynomial.Cyclotomic.Roots
 /-!
 # The Solution of a Cubic
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file proves Theorem 37 from the [100 Theorems List](https://www.cs.ru.nl/~freek/100/).
 
 In this file, we give the solutions to the cubic equation `a * x^3 + b * x^2 + c * x + d = 0`

mathlib commit https://github.com/leanprover-community/mathlib/commit/893964fc28cefbcffc7cb784ed00a2895b4e65cf

@@ -3,8 +3,8 @@ Copyright (c) 2022 Jeoff Lee. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeoff Lee
 
-! This file was ported from Lean 3 source module «100-theorems-list».«37_solution_of_cubic»
-! leanprover-community/mathlib commit 7fdeecc0d03cd40f7a165e6cf00a4d2286db599f
+! This file was ported from Lean 3 source module wiedijk_100_theorems.solution_of_cubic
+! leanprover-community/mathlib commit 5563b1b49e86e135e8c7b556da5ad2f5ff881cad
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

This lets us unify a few lemmas between GroupWithZero and EuclideanDomain and two lemmas that were previously proved separately for Nat, Int, Polynomial.

@@ -137,7 +137,7 @@ theorem cubic_eq_zero_iff_of_p_eq_zero (ha : a ≠ 0) (hω : IsPrimitiveRoot ω
       a * (x + b / (3 * a)) ^ 3 + (c - b ^ 2 / (3 * a)) * x + (d - b ^ 3 * a / (3 * a) ^ 3) := by
         field_simp; ring
       _ = a * (x + b / (3 * a)) ^ 3 + (d - (9 * a * b * c - 2 * b ^ 3) * a / (3 * a) ^ 3) := by
-        simp only [hb2, hb3]; field_simp; ring
+        simp only [hb2, hb3]; field_simp [ha]; ring
       _ = a * ((x + b / (3 * a)) ^ 3 - s ^ 3) := by rw [hs3, hq]; field_simp [h54]; ring
   have h₃ : ∀ x, a * x = 0 ↔ x = 0 := by intro x; simp [ha]
   have h₄ : ∀ x : K, x ^ 3 - s ^ 3 = (x - s) * (x - s * ω) * (x - s * ω ^ 2) := by

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -44,11 +44,8 @@ section Field
 open Polynomial
 
 variable {K : Type*} [Field K]
-
 variable [Invertible (2 : K)] [Invertible (3 : K)]
-
 variable (a b c d : K)
-
 variable {ω p q r s t : K}
 
 theorem cube_root_of_unity_sum (hω : IsPrimitiveRoot ω 3) : 1 + ω + ω ^ 2 = 0 := by

A random collection of changes, backporting from the upcoming Lean bump.

• squeeze one simp
• backport one more simp change (which probably was missed in the previous backports)
• rewrite the field_simp in SolutionOfCubic: with the upcoming Lean bump, this would become very slow

Similar to #10996 and #11001.

@@ -101,7 +101,6 @@ theorem cubic_eq_zero_iff (ha : a ≠ 0) (hω : IsPrimitiveRoot ω 3)
     a * x ^ 3 + b * x ^ 2 + c * x + d = 0 ↔
       x = s - t - b / (3 * a) ∨
         x = s * ω - t * ω ^ 2 - b / (3 * a) ∨ x = s * ω ^ 2 - t * ω - b / (3 * a) := by
-  have hi2 : (2 : K) ≠ 0 := nonzero_of_invertible _
   have hi3 : (3 : K) ≠ 0 := nonzero_of_invertible _
   have h9 : (9 : K) = 3 ^ 2 := by norm_num
   have h54 : (54 : K) = 2 * 3 ^ 3 := by norm_num
@@ -110,7 +109,9 @@ theorem cubic_eq_zero_iff (ha : a ≠ 0) (hω : IsPrimitiveRoot ω 3)
   have h₂ : ∀ x, a * x = 0 ↔ x = 0 := by intro x; simp [ha]
   have hp' : p = (3 * (c / a) - (b / a) ^ 2) / 9 := by field_simp [hp, h9]; ring_nf
   have hq' : q = (9 * (b / a) * (c / a) - 2 * (b / a) ^ 3 - 27 * (d / a)) / 54 := by
-    field_simp [hq, h54]; ring_nf
+    rw [hq, h54]
+    simp [field_simps, ha]
+    ring_nf
   rw [h₁, h₂, cubic_monic_eq_zero_iff (b / a) (c / a) (d / a) hω hp' hp_nonzero hq' hr hs3 ht x]
   have h₄ :=
     calc

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

@@ -87,7 +87,7 @@ theorem cubic_monic_eq_zero_iff (hω : IsPrimitiveRoot ω 3) (hp : p = (3 * c -
   have h54 : (54 : K) = 2 * 3 ^ 3 := by norm_num
   have h₁ : x ^ 3 + b * x ^ 2 + c * x + d = y ^ 3 + 3 * p * y - 2 * q := by
     rw [hp, hq]
-    field_simp [h9, h54]; ring
+    field_simp [y, h9, h54]; ring
   rw [h₁, cubic_basic_eq_zero_iff hω hp_nonzero hr hs3 ht y]
   simp_rw [eq_sub_iff_add_eq]
 #align theorems_100.cubic_monic_eq_zero_iff Theorems100.cubic_monic_eq_zero_iff

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -105,8 +105,8 @@ theorem cubic_eq_zero_iff (ha : a ≠ 0) (hω : IsPrimitiveRoot ω 3)
   have hi3 : (3 : K) ≠ 0 := nonzero_of_invertible _
   have h9 : (9 : K) = 3 ^ 2 := by norm_num
   have h54 : (54 : K) = 2 * 3 ^ 3 := by norm_num
-  have h₁ : a * x ^ 3 + b * x ^ 2 + c * x + d = a * (x ^ 3 + b / a * x ^ 2 + c / a * x + d / a) :=
-    by field_simp; ring
+  have h₁ : a * x ^ 3 + b * x ^ 2 + c * x + d
+    = a * (x ^ 3 + b / a * x ^ 2 + c / a * x + d / a) := by field_simp; ring
   have h₂ : ∀ x, a * x = 0 ↔ x = 0 := by intro x; simp [ha]
   have hp' : p = (3 * (c / a) - (b / a) ^ 2) / 9 := by field_simp [hp, h9]; ring_nf
   have hq' : q = (9 * (b / a) * (c / a) - 2 * (b / a) ^ 3 - 27 * (d / a)) / 54 := by
@@ -136,8 +136,8 @@ theorem cubic_eq_zero_iff_of_p_eq_zero (ha : a ≠ 0) (hω : IsPrimitiveRoot ω
   have h₂ :=
     calc
       a * x ^ 3 + b * x ^ 2 + c * x + d =
-          a * (x + b / (3 * a)) ^ 3 + (c - b ^ 2 / (3 * a)) * x + (d - b ^ 3 * a / (3 * a) ^ 3) :=
-        by field_simp; ring
+      a * (x + b / (3 * a)) ^ 3 + (c - b ^ 2 / (3 * a)) * x + (d - b ^ 3 * a / (3 * a) ^ 3) := by
+        field_simp; ring
       _ = a * (x + b / (3 * a)) ^ 3 + (d - (9 * a * b * c - 2 * b ^ 3) * a / (3 * a) ^ 3) := by
         simp only [hb2, hb3]; field_simp; ring
       _ = a * ((x + b / (3 * a)) ^ 3 - s ^ 3) := by rw [hs3, hq]; field_simp [h54]; ring

cliqueFree_of_replaceVertex_cliqueFree is still quite long.

@@ -43,7 +43,7 @@ section Field
 
 open Polynomial
 
-variable {K : Type _} [Field K]
+variable {K : Type*} [Field K]
 
 variable [Invertible (2 : K)] [Invertible (3 : K)]
 

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Jeoff Lee. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeoff Lee
-
-! This file was ported from Lean 3 source module wiedijk_100_theorems.solution_of_cubic
-! leanprover-community/mathlib commit 5563b1b49e86e135e8c7b556da5ad2f5ff881cad
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Tactic.LinearCombination
 import Mathlib.RingTheory.Polynomial.Cyclotomic.Roots
 
+#align_import wiedijk_100_theorems.solution_of_cubic from "leanprover-community/mathlib"@"5563b1b49e86e135e8c7b556da5ad2f5ff881cad"
+
 /-!
 # The Solution of a Cubic
 

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -134,7 +134,7 @@ theorem cubic_eq_zero_iff_of_p_eq_zero (ha : a ≠ 0) (hω : IsPrimitiveRoot ω
   have hi2 : (2 : K) ≠ 0 := nonzero_of_invertible _
   have hi3 : (3 : K) ≠ 0 := nonzero_of_invertible _
   have h54 : (54 : K) = 2 * 3 ^ 3 := by norm_num
-  have hb2 : b ^ 2 = 3 * a * c := by rw [sub_eq_zero] at hpz ; rw [hpz]
+  have hb2 : b ^ 2 = 3 * a * c := by rw [sub_eq_zero] at hpz; rw [hpz]
   have hb3 : b ^ 3 = 3 * a * b * c := by rw [pow_succ, hb2]; ring
   have h₂ :=
     calc

There is not really a standard negation for iff, but I think the one I have set up here is a common one, and anyway any handling is better than nothing.

If someone would like an alternate handling of the iff negation, they can set it up as an option for the tactic, as is currently done with the variants on the and negation.