Theorems · Theorem · number theory
ZLattice.covolume_eq_det
∀ {ι : Type u_2} [inst : Fintype ι] [inst_1 : DecidableEq ι] (L : Submodule ℤ (ι → ℝ)) [inst_2 : DiscreteTopology ↥L]
[IsZLattice ℝ L] (b : Module.Basis ι ℤ ↥L),
ZLattice.covolume L MeasureTheory.volume = |(Matrix.of (Subtype.val ∘ ⇑b)).det|- Defined in
- Mathlib.Algebra.Module.ZLattice.Covolume
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- CommRingproof · cited by 17,173
- Equivstatement and proof · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Submodulestatement and proof · cited by 7,192
- AddGroupproof · cited by 4,410
- Matrixstatement and proof · cited by 4,303
- absstatement and proof · cited by 1,814
- Module.Basisstatement and proof · cited by 1,477
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Latticeproof · cited by 916
Cited by3
Results whose statement or proof uses this declaration.
- NumberField.Units.regOfFamily_eq_det'proof · cited by 3
- ZLattice.covolume_div_covolume_eq_relIndexproof · cited by 2
- ZLattice.covolume_eq_det_invproof · cited by 1