Five normalized error symmetric
ProvedD1Bound5.five_normalized_error_symmetricdiophantine-tuplesnumber-theory
Symmetry survives the square-root normalization, with no nonzero hypotheses on tuple entries or auxiliary roots.
Preamble
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 import Definitions.Def_D1Bound5_DeterminantNormalization_Definitions
Formal statement
section
open Matrix
namespace D1Bound5
theorem _root_.D1Bound5.five_normalized_error_symmetric
(t u : Fin 5 → ℂ) (M : Matrix (Fin 5) (Fin 5) ℂ)
(hsym : Mᵀ = M) :
(normalizedRootError t u M)ᵀ = normalizedRootError t u M := by sorry
end D1Bound5
end
Source
D1Bound5/ProductFiveExactIdentity.lean, lines 19-32, SHA-256 6ac5997ec73913f4e6c11bdd843ec02784b0283e37205bd8579ba3bcc84fb6a8. Project: https://github.com/tomislav-math/d1-bound5-lean