Theorems · Theorem · convex and discrete geometry

AffineBasis.convexHull_eq_nonneg_coord

∀ {R : Type u_1} {E : Type u_3} [inst : Field R] [inst_1 : AddCommGroup E] [inst_2 : Module R E]
  [inst_3 : LinearOrder R] [IsStrictOrderedRing R] {ι : Type u_8} (b : AffineBasis ι R E),
  (convexHull R) (Set.range ⇑b) = {x | ∀ (i : ι), 0 ≤ (b.coord i) x}

The convex hull of an affine basis is the intersection of the half-spaces defined by the corresponding barycentric coordinates.

Defined in

Mathlib.Analysis.Convex.Combination

Cited by

1 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupModuleLinearOrderIsStrictOrderedRing