Theorems · Theorem · geometry

Finset.affineCombination_apply

∀ {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),
  (Finset.affineCombination k s p) w = (s.weightedVSubOfPoint p (Classical.choice ⋯)) w +ᵥ Classical.choice ⋯

Applying affineCombination with given weights. This is for the case where a result involving a default base point is OK (for example, when that base point will cancel out later); a more typical use case for affineCombination would involve selecting a preferred base point with affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one and then using weightedVSubOfPoint_apply.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

4 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor