Mathlib Map

Theorems · Definition · number theory

NumberField.mixedEmbedding.normAtPlace

{K : Type u_1} → [inst : Field K] → NumberField.InfinitePlace K → NumberField.mixedEmbedding.mixedSpace K →*₀ ℝ

The norm at the infinite place w of an element of the mixed space

Defined in
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
Cited by
45 results in Mathlib
Foundations
Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Field

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

NumberField.mixedEmbedding.norm · cited by 46mixedEmbedding.normNumberField.mixedEmbedding.normAtAllPlaces · cited by 30mixedEmbedding.normAtAllP…NumberField.mixedEmbedding.logMap · cited by 21mixedEmbedding.logMapNumberField.mixedEmbedding.convexBodySumFun · cited by 14mixedEmbedding.convexBody…NumberField.mixedEmbedding.normAtPlace_nonneg · cited by 11mixedEmbedding.normAtPlac…NumberField.mixedEmbedding.normAtPlace_apply_of_isComplex · cited by 9mixedEmbedding.normAtPlac…NumberField.mixedEmbedding.normAtPlace_apply · cited by 8mixedEmbedding.normAtPlac…NumberField.mixedEmbedding.normAtPlace_apply_of_isReal · cited by 8mixedEmbedding.normAtPlac…NumberField.mixedEmbedding.normAtComplexPlaces · cited by 8mixedEmbedding.normAtComp…NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace · cited by 6mixedEmbedding.normAtPlac…NumberField.mixedEmbedding.normAtPlace_smul · cited by 5mixedEmbedding.normAtPlac…NumberField.mixedEmbedding.norm_smul · cited by 5mixedEmbedding.norm_smulNumberField.mixedEmbedding.norm_eq_of_normAtPlace_eq · cited by 3mixedEmbedding.norm_eq_of…NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces · cited by 3fundamentalCone.norm_norm…NumberField.mixedEmbedding.continuous_normAtPlace · cited by 3mixedEmbedding.continuous…Real · cited by 25697RealField · cited by 7404FieldComplex · cited by 5565ComplexNorm.norm · cited by 5413Norm.normMonoidWithZeroHom · cited by 704MonoidWithZeroHomNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceNumberField.InfinitePlace.IsReal · cited by 301InfinitePlace.IsRealNumberField.InfinitePlace.IsComplex · cited by 272InfinitePlace.IsComplexNumberField.mixedEmbedding.mixedSpace · cited by 239mixedEmbedding.mixedSpacemixedEmbedding.normAtPlaceCITED BYCITES

Cites9

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Cited by50

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