ceil — Mathlib

English

The i-th coordinate of floor b m equals the floor of the i-th coordinate of m with respect to b.

Русский

i-я координата floor b m равна округлению вниз i-й координаты m в базисе b.

LaTeX

$$$ b.repr(\operatorname{floor}_b(m))_i = \Big\lfloor b.repr(m)_i \Big\rfloor $$$

Lean4

/-- 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`. -/
def ceil (m : E) : span ℤ (Set.range b) :=
  ∑ i, ⌈b.repr m i⌉ • b.restrictScalars ℤ i

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