Theorems · Definition · number theory

NumberField.mixedEmbedding.polarCoord

(K : Type u_1) →
  [inst : Field K] →
    [NumberField K] →
      OpenPartialHomeomorph (NumberField.mixedEmbedding.mixedSpace K) (NumberField.mixedEmbedding.realMixedSpace K)

The polar coordinate open partial homeomorphism between the mixed space ℝ^r₁ × ℂ^r₂ and ℝ^r₁ × (ℝ × ℝ)^r₂ defined as the identity on the first component and mapping (zᵢ)ᵢ to (‖zᵢ‖, Arg zᵢ)ᵢ on the second component.

Defined in

Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord

Cited by

15 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldNumberField