Signed entry good or neg
ProvedD1Bound5.signed_entry_good_or_negdiophantine-tuplesnumber-theory
One of the two integral signs satisfies both normalized bounds. The proof uses only the two possible signs of an existing root.
Preamble
import Mathlib.Analysis.Complex.Basic import Mathlib.Analysis.Complex.Polynomial.Basic import Mathlib.Data.Complex.Basic import Mathlib.LinearAlgebra.Matrix.Determinant.Basic import Mathlib.Tactic.FieldSimp import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Mathlib.Tactic.NormNum import Mathlib.Tactic.Ring import Definitions.Def_D1Bound5_RootMatrixSigns_Definitions
Formal statement
section
namespace D1Bound5
theorem _root_.D1Bound5.signed_entry_good_or_neg {R : Type*} [CommRing R]
(f : R →+* ℂ) (a b r : R) (u v : ℂ)
(hu : u^2 = f a) (hv : v^2 = f b)
(hr : r^2 = a*b+1) (hab : 9 ≤ ‖f a * f b‖) :
SignedEntryGood f a b u v r ∨ SignedEntryGood f a b u v (-r) := by sorry
end D1Bound5
namespace D1Bound5
end D1Bound5
namespace D1Bound5
end D1Bound5
end
Source
D1Bound5/RootMatrixSigns.lean, lines 12-31, SHA-256 ebdfe7f3d298bcbeeffe34affc4b69cd64eed73b495d78d2fa97d30c70560fcd. Project: https://github.com/tomislav-math/d1-bound5-lean