Theorems · Theorem · geometry

Affine.Simplex.affineIndependent_points_update_centroid

∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : DivisionRing k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] {n : ℕ} [CharZero k] (s : Affine.Simplex k P n) (i : Fin (n + 1)),
  AffineIndependent k (Function.update s.points i s.centroid)

Replacing a vertex of a simplex by its centroid preserves affine independence.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid

Cited by

1 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddTorsorCharZero