Finset.sum_centroidWeights_eq_one_of_card_ne_zero
∀ (k : Type u_1) [inst : DivisionRing k] {ι : Type u_4} (s : Finset ι) [CharZero k],
s.card ≠ 0 → ∑ i ∈ s, Finset.centroidWeights k s i = 1In the characteristic zero case, the weights in the centroid sum to 1 if the number of points is not zero.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRingCharZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.sumstatement · cited by 5,195
- Finset.cardstatement and proof · cited by 2,327
- DivisionRingstatement and proof · cited by 1,062
- CharZerostatement and proof · cited by 932
- nsmul_eq_mulproof · cited by 369
- Finset.sum_constproof · cited by 254
- mul_inv_cancel₀proof · cited by 210
- Finset.centroidWeightsstatement · cited by 27
Cited by6
Results whose statement or proof uses this declaration.
- Finset.sum_centroidWeights_eq_one_of_nonemptyproof · cited by 8
- Affine.Simplex.centroid_mapproof · cited by 3
- Affine.Simplex.faceOppositeCentroid_mapproof · cited by 3
- Finset.sum_centroidWeights_eq_one_of_card_eq_add_oneproof · cited by 2
- centroid_mem_affineSpan_of_card_ne_zeroproof · cited by 0
- Finset.sum_centroidWeightsIndicator_eq_one_of_card_ne_zeroproof · cited by 0