Theorems · Theorem · convex and discrete geometry

Convexity.IsModuleConvexSpace.sConvexComb_eq_sum

∀ {R : Type u_2} {M : Type u_3} {inst : Semiring R} {inst_1 : PartialOrder R} {inst_2 : IsStrictOrderedRing R}
  {inst_3 : AddCommMonoid M} {inst_4 : Module R M} {inst_5 : Convexity.ConvexSpace R M}
  [self : Convexity.IsModuleConvexSpace R M] (w : Convexity.StdSimplex R M),
  Convexity.sConvexComb w = w.weights.sum fun m r => r • m

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Module

Cited by

7 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Convexity.IsModuleConvexSpace