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Quad Int — complex image

Proved
D1Bound5.QuadInt.complex_image

by tp · Oct 23, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

The image of an arbitrary coordinate element under a complex ring map.

Preamble
import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Analysis.Complex.Norm
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Definitions.Def_D1Bound5_Coordinates_Definitions

Formal statement
section
namespace D1Bound5.QuadInt

open scoped QuadraticAlgebra

variable {tau nu : ℤ}


theorem _root_.D1Bound5.QuadInt.complex_image (f : QuadInt tau nu →+* ℂ) (z : QuadInt tau nu) :
    f z = (z.re : ℂ)+(z.im : ℂ)*f QuadraticAlgebra.omega := by sorry









end D1Bound5.QuadInt
end
Source
D1Bound5/ComplexCoordinates.lean, lines 11-18, SHA-256 1683447b1e232bc1f4d7a3f22a33ac3030c9c47df02e5a5ff8d90857c32c1858. Project: https://github.com/tomislav-math/d1-bound5-lean

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