Theorems · Definition · number theory

NumberField.mixedEmbedding.polarSpaceCoord

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

The polar coordinate open partial homeomorphism between the mixed space ℝ^r₁ × ℂ^r₂ and the polar space ℝ^(r₁ + r₂) × ℝ^r₂ defined by sending x to x w or ‖x w‖ depending on whether w is real or complex for the first component, and to Arg (x w), w complex, for the second component.

Defined in

Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord

Cited by

11 results in Mathlib

Foundations

Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldNumberField