Introduction

 
Simplicial Complexes
      SimplicialComplex(f) : SeqEnum[SetEnum] -> SmpCpx
      Example SmpCpx_construct (H153E1)
      SimplicialComplex(G) : Grph -> SmpCpx
      FlagComplex(G) : Grph -> SmpCpx
      Dimension(X) : SmpCpx -> RngIntElt
      Example SmpCpx_dimension (H153E2)
      Faces(X, d) : SmpCpx, RngIntElt -> SeqEnum[SetEnum]
      Example SmpCpx_faces (H153E3)
      Facets(X) : SmpCpx -> SeqEnum[SetEnum]
      Example SmpCpx_facets (H153E4)
      Normalization(X) : SmpCpx -> SmpCpx
      Shift(X, n) : SmpCpx, RngIntElt -> SmpCpx
      Example SmpCpx_normalize-shift (H153E5)
      Boundary(X) : SmpCpx -> SmpCpx
      Example SmpCpx_boundary (H153E6)
      S + T : SmpCpx, SmpCpx -> SmpCpx
      Example SmpCpx_sum (H153E7)
      S eq T : SmpCpx, SmpCpx -> BoolElt
      Example SmpCpx_eq (H153E8)
      Product(S,T) : SmpCpx, SmpCpx -> SmpCpx
      Example SmpCpx_product (H153E9)
      Join(S,T) : SmpCpx, SmpCpx -> SmpCpx
      Example SmpCpx_join (H153E10)
      AddSimplex(X, s) : SmpCpx, SetEnum -> SmpCpx
      Prune(X, f) : SmpCpx, SetEnum -> SmpCpx
      Glue(X, e) : SmpCpx, SeqEnum -> SmpCpx
      Example SmpCpx_prune-glue (H153E11)
      BarycentricSubdivision(X) : SmpCpx -> SmpCpx
      Skeleton(X, q) : SmpCpx, RngIntElt -> SmpCpx
      UnderlyingGraph(X) : SmpCpx -> GrphUnd, GrphVertSet, GrphEdgeSet
      Cone(X) : SmpCpx -> SmpCpx
      Suspension(X) : SmpCpx -> SmpCpx
      Example SmpCpx_cone-suspension (H153E12)

      Standard Topological Objects
            Simplex(n) : RngIntElt -> SmpCpx
            Sphere(n) : RngIntElt -> SmpCpx
            KleinBottle() : -> SmpCpx
            Torus() : -> SmpCpx
            Cylinder() : -> SmpCpx
            MoebiusStrip() : -> SmpCpx
            LensSpace(p) : RngIntElt -> SmpCpx
            SimplicialProjectivePlane() : -> SmpCpx

 
Homology Computation
      Homology(X) : SmpCpx -> SeqEnum, SeqEnum
      Example SmpCpx_homology (H153E13)
      HomologyGroup(X, q) : SmpCpx, RngIntElt -> ModRng
      BettiNumber(X,q) : SmpCpx, RngIntElt -> RngIntElt
      TorsionCoefficients(X, q) : SmpCpx, RngIntElt -> SeqEnum[RngElt]
      EulerCharacteristic(X) : SmpCpx -> RngIntElt
      BoundaryMatrix(X, q, A) : SmpCpx, RngIntElt, Rng -> Mtrx
      ChainComplex(X, A) : SmpCpx, Rng -> ModCpx
      Example SmpCpx_chaincomplex (H153E14)
      HomologyGenerators(X) : SmpCpx ->
      Example SmpCpx_homologygenerators (H153E15)

 
Bibliography

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