Theorems · Theorem · geometry

Affine.Simplex.faceOppositeCentroid_map

∀ {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] [CharZero k] {V₂ : Type u_4} {P₂ : Type u_5} [inst_5 : AddCommGroup V₂]
  [inst_6 : Module k V₂] [inst_7 : AddTorsor V₂ P₂] {n : ℕ} [inst_8 : NeZero n] (s : Affine.Simplex k P n)
  (f : P →ᵃ[k] P₂) (hf : Function.Injective ⇑f) {i : Fin (n + 1)},
  (s.map f hf).faceOppositeCentroid i = f (s.faceOppositeCentroid i)

Defined in

Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid

Cited by

3 results in Mathlib

Foundations

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

Assumes

DivisionRingAddCommGroupModuleAddTorsorCharZeroAddCommGroupModuleAddTorsorNeZero