Exists normalized quadratic ring equiv
ProvedD1Bound5.exists_normalized_quadratic_ring_equivdiophantine-tuplesnumber-theory
Every quadratic number ring has normalized integral coordinates with trace zero or one. No maximal-order or discriminant condition is assumed.
Preamble
import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Data.Int.GCD import Mathlib.LinearAlgebra.Dimension.Free import Mathlib.NumberTheory.NumberField.Norm import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Definitions.Def_D1Bound5_Coordinates_Definitions
Formal statement
section
open scoped NumberField
open Module
namespace D1Bound5
variable {K : Type*} [Field K] [NumberField K]
theorem _root_.D1Bound5.exists_normalized_quadratic_ring_equiv (hK : finrank ℚ K = 2) :
∃ tau nu : ℤ, (tau = 0 ∨ tau = 1) ∧ Nonempty (QuadInt tau nu ≃+* 𝓞 K) := by sorry
end D1Bound5
end
Source
D1Bound5/FullRingBasis.lean, lines 116-123, SHA-256 7a7a55f350ab7d5224275914efa11b126ec34a9ae9cc9e505c2669503411924c. Project: https://github.com/tomislav-math/d1-bound5-lean