Theorems · Theorem · geometry

Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_one

∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [S : AddTorsor V P] {ι : Type u_4} (s : Finset ι) (w : ι → k) (p : ι → P),
  ∑ i ∈ s, w i = 1 → ∀ (b₁ b₂ : P), (s.weightedVSubOfPoint p b₁) w +ᵥ b₁ = (s.weightedVSubOfPoint p b₂) w +ᵥ b₂

The weighted sum, added to the base point, is independent of the base point when the sum of the weights is 1.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

2 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor