Theorems · Definition · geometry
spanPoints
(k : Type u_1) →
{V : Type u_2} →
{P : Type u_3} → [inst : Ring k] → [inst_1 : AddCommGroup V] → [Module k V] → [AddTorsor V P] → Set P → Set PThe points in the affine span of a (possibly empty) set of points. Use affineSpan instead to
get an AffineSubspace k P.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Set.ofPredproof · cited by 6,101
- HVAdd.hVAddproof · cited by 1,820
- AddTorsorstatement and proof · cited by 1,657
- vectorSpanproof · cited by 123
Cited by8
Results whose statement or proof uses this declaration.
- affineSpanproof · cited by 417
- subset_spanPointsstatement · cited by 4
- mem_spanPointsstatement · cited by 2
- vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPointsstatement and proof · cited by 1
- AffineSubspace.spanPoints_subset_coe_of_subset_coestatement and proof · cited by 1
- vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpanstatement and proof · cited by 1
- spanPoints_nonemptystatement and proof · cited by 1
- coe_affineSpanstatement · cited by 0