Near Half off Diagonal cofactor bound
ProvedD1Bound5.nearHalf_offDiagonal_cofactor_bounddiophantine-tuplesnumber-theory
A precise off-diagonal cofactor estimate for six complex entries near 1/2.
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
namespace D1Bound5
theorem _root_.D1Bound5.nearHalf_offDiagonal_cofactor_bound (x y z u v w : 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))
(hu : ‖u - (1/2 : ℂ)‖ < (128/8649 : ℝ))
(hv : ‖v - (1/2 : ℂ)‖ < (128/8649 : ℝ))
(hw : ‖w - (1/2 : ℂ)‖ < (128/8649 : ℝ)) :
‖w^2*x - w*z*u - w*y*v + (1/8 : ℂ)‖ < (197/10000 : ℝ) := by sorry
end D1Bound5
end
Source
D1Bound5/AdjugateOffDiagonal.lean, lines 6-128, SHA-256 8c486c90daafb9dd89af32dc3fe1f2ba55d55fc2b7397544af7a0ac1e04b8b6f. Project: https://github.com/tomislav-math/d1-bound5-lean