Finset.sum_centroidWeights_eq_one_of_nonempty
∀ (k : Type u_1) [inst : DivisionRing k] {ι : Type u_4} (s : Finset ι) [CharZero k],
s.Nonempty → ∑ i ∈ s, Finset.centroidWeights k s i = 1In the characteristic zero case, the weights in the centroid sum to 1 if the set is nonempty.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 62 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
- DivisionRingstatement and proof · cited by 1,062
- Finset.Nonemptystatement and proof · cited by 1,001
- CharZerostatement and proof · cited by 932
- ne_of_gtproof · cited by 637
- Finset.card_posproof · cited by 53
- Finset.centroidWeightsstatement · cited by 27
- Finset.sum_centroidWeights_eq_one_of_card_ne_zeroproof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- Affine.Simplex.centroid_vsub_eqproof · cited by 4
- Finset.centroid_eq_centerMassproof · cited by 2
- Affine.Simplex.centroid_notMem_affineSpan_of_ne_univproof · cited by 1
- Affine.Simplex.sum_centroidWeightsWithCircumcenterproof · cited by 1
- AffineBasis.coord_apply_centroidproof · cited by 1
- Finset.centroid_vsub_constproof · cited by 1
- centroid_mem_affineSpan_of_nonemptyproof · cited by 0
- Finset.sum_centroidWeightsIndicator_eq_one_of_nonemptyproof · cited by 0