Theorems · Theorem · geometry

Affine.Simplex.affineCombination_mem_interior_iff

∀ {k : Type u_1} {V : Type u_2} {P : Type u_4} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] [inst_4 : PartialOrder k] {n : ℕ} {s : Affine.Simplex k P n} {w : Fin (n + 1) → k},
  ∑ i, w i = 1 →
    ((Finset.affineCombination k Finset.univ s.points) w ∈ s.interior ↔ ∀ (i : Fin (n + 1)), w i ∈ Set.Ioo 0 1)

Defined in

Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic

Cited by

4 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsorPartialOrder