Theorems · Definition · convex and discrete geometry

PointedCone.hull

(R : Type u_1) →
  {E : Type u_2} →
    [inst : Semiring R] →
      [inst_1 : PartialOrder R] →
        [inst_2 : IsOrderedRing R] → [inst_3 : AddCommMonoid E] → [inst_4 : Module R E] → Set E → PointedCone R E

The cone hull of a set s is the smallest pointed cone that contains s. Pointed cones being defined as submodules over nonnegative scalars, this is implemented as the submodule span of s w.r.t. nonnegative scalars.

Defined in

Mathlib.Geometry.Convex.Cone.Pointed

Cited by

12 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsOrderedRingAddCommMonoidModule