Quad Int norm add le twice
ProvedD1Bound5.quadInt_norm_add_le_twicediophantine-tuplesnumber-theory
The norm parallelogram identity gives a division-free root bound.
Preamble
import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Algebra.Ring.Basic import Mathlib.Algebra.Ring.Equiv import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Prod import Mathlib.Data.Int.Interval import Mathlib.Data.Int.Sqrt import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Definitions.Def_D1Bound5_Coordinates_Definitions
Formal statement
section
namespace D1Bound5
open QuadInt
theorem _root_.D1Bound5.quadInt_norm_add_le_twice {tau nu : ℤ}
(hd : 0 < discriminant tau nu) (x y : QuadInt tau nu) :
(x+y).norm ≤ 2*x.norm+2*y.norm := by sorry
end D1Bound5
end
Source
D1Bound5/PairExtensionCore.lean, lines 12-21, SHA-256 d45446b353f1adcd08c1943cfe73040bef48ad11485fc541c7388b34f9e5255f. Project: https://github.com/tomislav-math/d1-bound5-lean