Theorems · Theorem · geometry

Finset.weightedVSubOfPoint_apply_const

∀ {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 b : P),
  (s.weightedVSubOfPoint (fun x => p) b) w = (∑ i ∈ s, w i) • (p -ᵥ b)

The value of weightedVSubOfPoint, where the given points are equal.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

4 results in Mathlib

Foundations

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

Assumes

RingAddCommGroupModuleAddTorsor