Theorems · Theorem · number theory

NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K]
  (I : (FractionalIdeal (nonZeroDivisors (NumberField.RingOfIntegers K)) K)ˣ),
  MeasureTheory.volume (ZSpan.fundamentalDomain (NumberField.mixedEmbedding.fractionalIdealLatticeBasis K I)) =
    ENNReal.ofReal ↑(FractionalIdeal.absNorm ↑I) *
      MeasureTheory.volume (ZSpan.fundamentalDomain (NumberField.mixedEmbedding.latticeBasis K))

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody
Cited by: 3 results in Mathlib
Foundations: Depth 310 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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DFunLike.coestatement and proof · cited by 62,936
Setstatement and proof · cited by 53,352
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ENNRealstatement and proof · cited by 9,879
Equivproof · cited by 8,337
Fieldstatement and proof · cited by 7,404
Submodulestatement · cited by 7,192
Complexstatement · cited by 5,565
Equiv.symmproof · cited by 3,681
Unitsstatement and proof · cited by 2,804
Units.valstatement and proof · cited by 1,966

Cited by3

Results whose statement or proof uses this declaration.

NumberField.hermiteTheorem.minkowskiBound_lt_boundOfDiscBddproof · cited by 2
NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discrproof · cited by 2
NumberField.mixedEmbedding.covolume_idealLatticeproof · cited by 1