Theorems · Definition · convex and discrete geometry

PointedCone.dual

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

The dual cone of a set s with respect to a bilinear pairing p is the cone consisting of all points y such that for all points x ∈ s we have 0 ≤ p x y.

Defined in

Mathlib.Geometry.Convex.Cone.Dual

Cited by

47 results in Mathlib

Foundations

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

Assumes

CommSemiringPartialOrderIsOrderedRingAddCommMonoidModuleAddCommMonoidModule