Quad Int — four norm
ProvedD1Bound5.QuadInt.four_normdiophantine-tuplesnumber-theory
Equation (integrated-disk), completed-square identity.
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.four_norm (z : QuadInt tau nu) :
4*z.norm = (2*z.re+tau*z.im)^2 + discriminant tau nu*z.im^2 := by sorry
end QuadInt
end D1Bound5
end
Source
D1Bound5/Coordinates.lean, lines 23-28, SHA-256 da0cb0c42a6044e813dcdaaa1831735e6baddba8fa16b037f5289e53bcfae065. Project: https://github.com/tomislav-math/d1-bound5-lean