Near Half triple cofactor bound
ProvedD1Bound5.nearHalf_triple_cofactor_bounddiophantine-tuplesnumber-theory
Uniform diagonal cofactor error for three entries near one half.
Preamble
import Lean.Util.CollectAxioms import Mathlib.Analysis.CStarAlgebra.Matrix import Mathlib.Analysis.Complex.Basic import Mathlib.Analysis.Complex.Polynomial.Basic import Mathlib.Analysis.InnerProductSpace.PiL2 import Mathlib.Analysis.SpecificLimits.Normed import Mathlib.Data.Complex.Basic import Mathlib.LinearAlgebra.Matrix.Determinant.Basic import Mathlib.LinearAlgebra.Matrix.NonsingularInverse import Mathlib.LinearAlgebra.Matrix.Permutation import Mathlib.LinearAlgebra.Matrix.SchurComplement import Mathlib.Tactic.FieldSimp import Mathlib.Tactic.FinCases import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Mathlib.Tactic.NormNum import Mathlib.Tactic.Ring
Formal statement
section
open scoped Matrix.Norms.L2Operator
open Matrix
namespace D1Bound5
end D1Bound5
namespace D1Bound5
end D1Bound5
namespace D1Bound5
theorem _root_.D1Bound5.nearHalf_triple_cofactor_bound (x y z : ℂ)
(hx : ‖x - (1/2 : ℂ)‖ < (128/8649 : ℝ))
(hy : ‖y - (1/2 : ℂ)‖ < (128/8649 : ℝ))
(hz : ‖z - (1/2 : ℂ)‖ < (128/8649 : ℝ)) :
‖2*x*y*z - (1/4 : ℂ)‖ < (23/1000 : ℝ) := by sorry
end D1Bound5
end
Source
D1Bound5/AdjugateFourBounds.lean, lines 112-180, SHA-256 e5781cd0cc609ab6e464413c644de534702a0bca3e48c68b9e060b00a6b88c13. Project: https://github.com/tomislav-math/d1-bound5-lean