Mathlib Map

Theorems · Definition · number theory

NumberField.mixedEmbedding

(K : Type u_1) → [inst : Field K] → K →+* NumberField.mixedEmbedding.mixedSpace K

The mixed embedding of a number field K into the mixed space of K.

Defined in
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
Cited by
52 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.fractionalIdealLatticeBasis · cited by 11mixedEmbedding.fractional…NumberField.mixedEmbedding.normAtPlace_apply · cited by 8mixedEmbedding.normAtPlac…NumberField.mixedEmbedding.norm_eq_norm · cited by 7mixedEmbedding.norm_eq_no…NumberField.mixedEmbedding.unitSMul_smul · cited by 6mixedEmbedding.unitSMul_s…NumberField.mixedEmbedding.idealLattice · cited by 6mixedEmbedding.idealLatti…NumberField.mixedEmbedding_injective · cited by 6NumberField.mixedEmbeddin…NumberField.mixedEmbedding.fundamentalCone.completeFamily · cited by 5fundamentalCone.completeF…NumberField.mixedEmbedding.fundamentalCone.mixedEmbedding_preimageOfMemIntegerSet · cited by 5fundamentalCone.mixedEmbe…NumberField.mixedEmbedding.integerLattice · cited by 5mixedEmbedding.integerLat…NumberField.mixedEmbedding.fundamentalCone.mem_integerSet · cited by 4fundamentalCone.mem_integ…NumberField.mixedEmbedding.latticeBasis_apply · cited by 4mixedEmbedding.latticeBas…NumberField.mixedEmbedding.normAtAllPlaces_mixedEmbedding · cited by 4mixedEmbedding.normAtAllP…NumberField.mixedEmbedding.norm_unit · cited by 3mixedEmbedding.norm_unitNumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis · cited by 3mixedEmbedding.volume_fun…NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne · cited by 3fundamentalCone.completeB…Real · cited by 25697RealRingHom · cited by 10189RingHomField · cited by 7404FieldComplex · cited by 5565ComplexNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceNumberField.InfinitePlace.IsReal · cited by 301InfinitePlace.IsRealNumberField.InfinitePlace.IsComplex · cited by 272InfinitePlace.IsComplexNumberField.mixedEmbedding.mixedSpace · cited by 239mixedEmbedding.mixedSpaceNumberField.InfinitePlace.embedding · cited by 78InfinitePlace.embeddingRingHom.pi · cited by 26RingHom.piNumberField.InfinitePlace.embedding_of_isReal · cited by 12InfinitePlace.embedding_o…RingHom.prod · cited by 8RingHom.prodNumberField.mixedEmbeddingCITED BYCITES

Cites12

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

Cited by56

Results whose statement or proof uses this declaration.