Theorems · Theorem · number theory

NumberField.mixedEmbedding.polarCoord_symm_apply

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K]
  (p : ({ w // w.IsReal } → ℝ) × ({ w // w.IsComplex } → ℝ × ℝ)),
  ↑(NumberField.mixedEmbedding.polarCoord K).symm p = (p.1, Pi.map (fun i => ↑Complex.polarCoord.symm) p.2)

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord
Cited by: 4 results in Mathlib
Foundations: Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites14

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Realstatement and proof · cited by 25,697
Fieldstatement and proof · cited by 7,404
Complexstatement · cited by 5,565
OpenPartialHomeomorph.toFun'statement and proof · cited by 745
NumberFieldstatement and proof · cited by 653
NumberField.InfinitePlacestatement and proof · cited by 604
OpenPartialHomeomorph.symmstatement and proof · cited by 460
NumberField.InfinitePlace.IsRealstatement and proof · cited by 301
NumberField.InfinitePlace.IsComplexstatement and proof · cited by 272
NumberField.mixedEmbedding.mixedSpacestatement · cited by 239
Pi.mapstatement · cited by 60
NumberField.mixedEmbedding.realMixedSpacestatement · cited by 34

Cited by4

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.lintegral_comp_polarSpaceCoord_symmproof · cited by 1
NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isRealproof · cited by 0
NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isComplexproof · cited by 0
NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symmproof · cited by 0