Theorems · Definition · number theory

ZSpan.ceil

{E : Type u_1} →
  {ι : Type u_2} →
    {K : Type u_3} →
      [inst : NormedField K] →
        [inst_1 : NormedAddCommGroup E] →
          [inst_2 : NormedSpace K E] →
            (b : Module.Basis ι K E) →
              [inst_3 : LinearOrder K] →
                [IsStrictOrderedRing K] → [FloorRing K] → [Fintype ι] → E → ↥(Submodule.span ℤ (Set.range ⇑b))

The map that sends a vector of E to the element of the ℤ-lattice spanned by b obtained by rounding up its coordinates on the basis b.

Defined in

Mathlib.Algebra.Module.ZLattice.Basic

Cited by

3 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNormedAddCommGroupNormedSpaceLinearOrderIsStrictOrderedRingFloorRingFintype