Mathlib Map

Theorems · Definition · geometry

AffineBasis.coord

{ι : Type u_1} →
  {k : Type u_5} →
    {V : Type u_6} →
      {P : Type u_7} →
        [inst : AddCommGroup V] →
          [inst_1 : AddTorsor V P] → [inst_2 : Ring k] → [inst_3 : Module k V] → AffineBasis ι k P → ι → P →ᵃ[k] k

The ith barycentric coordinate of a point.

Defined in
Mathlib.LinearAlgebra.AffineSpace.Basis
Cited by
26 results in Mathlib
Foundations
Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommGroupAddTorsorRingModule

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AffineBasis.toMatrix · cited by 11AffineBasis.toMatrixAffineBasis.coord_apply_combination_of_mem · cited by 6AffineBasis.coord_apply_c…AffineBasis.sum_coord_apply_eq_one · cited by 4AffineBasis.sum_coord_app…AffineBasis.coord_apply · cited by 4AffineBasis.coord_applyAffineBasis.coords · cited by 4AffineBasis.coordsAffineBasis.affineCombination_coord_eq_self · cited by 3AffineBasis.affineCombina…AffineBasis.toMatrix_apply · cited by 2AffineBasis.toMatrix_applyAffineBasis.toMatrix_vecMul_coords · cited by 2AffineBasis.toMatrix_vecM…continuous_barycentric_coord · cited by 2continuous_barycentric_co…AffineBasis.surjective_coord · cited by 1AffineBasis.surjective_co…AffineBasis.affineIndependent_of_toMatrix_right_inv · cited by 1AffineBasis.affineIndepen…AffineBasis.affineSpan_eq_top_of_toMatrix_left_inv · cited by 1AffineBasis.affineSpan_eq…isOpenMap_barycentric_coord · cited by 1isOpenMap_barycentric_coo…AffineBasis.coe_coord_of_subsingleton_eq_one · cited by 1AffineBasis.coe_coord_of_…AffineBasis.convexHull_eq_nonneg_coord · cited by 1AffineBasis.convexHull_eq…DFunLike.coe · cited by 62936DFunLike.coeModule · cited by 20661ModuleAddCommGroup · cited by 12871AddCommGroupRing · cited by 7463RingAddTorsor · cited by 1657AddTorsorVSub.vsub · cited by 817VSub.vsubAffineMap · cited by 674AffineMapAffineBasis · cited by 65AffineBasisAffineBasis.basisOf · cited by 11AffineBasis.basisOfModule.Basis.sumCoords · cited by 10Basis.sumCoordsAffineBasis.coordCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by28

Results whose statement or proof uses this declaration.