Theorems · Theorem · number theory
NumberField.mixedEmbedding.polarCoord_apply
∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K] (p : ({ w // w.IsReal } → ℝ) × ({ w // w.IsComplex } → ℂ)),
↑(NumberField.mixedEmbedding.polarCoord K) p = (p.1, Pi.map (fun i => ↑Complex.polarCoord) p.2)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
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Cites13
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 and proof · 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
- 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
- Complex.polarCoordstatement · cited by 26
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