Theorems · Definition · convex and discrete geometry

ConvexCone.IsGenerating

Deprecated since 2026-03-30Mathlib marks this declaration as deprecated.

{R : Type u_2} →
  {M : Type u_4} →
    [inst : Semiring R] →
      [inst_1 : PartialOrder R] → [inst_2 : AddCommMonoid M] → [inst_3 : Module R M] → ConvexCone R M → Prop

A convex cone C is generating if its linear span is the entire R-module M. IsGenerating is equivalent to IsReproducing modulo some conditions. See IsReproducing.isGenerating and IsGenerating.isReproducing for details.

Defined in

Mathlib.Geometry.Convex.Cone.Basic

Cited by

7 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Quot.sound

Assumes

SemiringPartialOrderAddCommMonoidModule