Theorems · Definition · convex and discrete geometry

PointedCone.DualFG

{R : Type u_1} →
  {M : Type u_2} →
    {N : Type u_3} →
      [inst : CommRing R] →
        [inst_1 : PartialOrder R] →
          [inst_2 : IsOrderedRing R] →
            [inst_3 : AddCommGroup M] →
              [inst_4 : Module R M] →
                [inst_5 : AddCommGroup N] → [inst_6 : Module R N] → (M →ₗ[R] N →ₗ[R] R) → PointedCone R N → Prop

A cone is dually finitely generated (DualFG) if it is the dual of a finite set. Equivalently, the cone can be written as the intersection of finitely many halfspace. It is also known as an H-cone. This is the counterpart to FG (finitely generated) which states that the cone is the span of a finite set, or a V-cone.

Defined in

Mathlib.Geometry.Convex.Cone.DualFinite

Cited by

11 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingPartialOrderIsOrderedRingAddCommGroupModuleAddCommGroupModule