Quad Int — discriminant le four bound
ProvedD1Bound5.QuadInt.discriminant_le_four_bounddiophantine-tuplesnumber-theory
A nonreal element in a bounded disk bounds the field discriminant. Used for the Delta<=60 reduction in lem:tail-irregular.
Preamble
import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Tactic.Linarith import Definitions.Def_D1Bound5_Coordinates_Definitions
Formal statement
section
namespace D1Bound5
namespace QuadInt
variable {tau nu : ℤ}
theorem _root_.D1Bound5.QuadInt.discriminant_le_four_bound (hd : 0 < discriminant tau nu)
{z : QuadInt tau nu} {M : ℤ} (hM : z.norm ≤ M) (hy : z.im ≠ 0) :
discriminant tau nu ≤ 4*M := by sorry
end QuadInt
end D1Bound5
end
Source
D1Bound5/Coordinates.lean, lines 64-73, SHA-256 da0cb0c42a6044e813dcdaaa1831735e6baddba8fa16b037f5289e53bcfae065. Project: https://github.com/tomislav-math/d1-bound5-lean