- Introduction
- Simplicial Complexes
- SimplicialComplex(f) : SeqEnum[SetEnum] -> SmpCpx
- Example SmpCpx_construct (H149E1)
- SimplicialComplex(G) : Grph -> SmpCpx
- FlagComplex(G) : Grph -> SmpCpx
- Dimension(X) : SmpCpx -> RngIntElt
- Example SmpCpx_dimension (H149E2)
- Faces(X, d) : SmpCpx, RngIntElt -> SeqEnum[SetEnum]
- Example SmpCpx_faces (H149E3)
- Facets(X) : SmpCpx -> SeqEnum[SetEnum]
- Example SmpCpx_facets (H149E4)
- Normalization(X) : SmpCpx -> SmpCpx
- Shift(X, n) : SmpCpx, RngIntElt -> SmpCpx
- Example SmpCpx_normalize-shift (H149E5)
- Boundary(X) : SmpCpx -> SmpCpx
- Example SmpCpx_boundary (H149E6)
- S + T : SmpCpx, SmpCpx -> SmpCpx
- Example SmpCpx_sum (H149E7)
- S eq T : SmpCpx, SmpCpx -> BoolElt
- Example SmpCpx_eq (H149E8)
- Product(S,T) : SmpCpx, SmpCpx -> SmpCpx
- Example SmpCpx_product (H149E9)
- Join(S,T) : SmpCpx, SmpCpx -> SmpCpx
- Example SmpCpx_join (H149E10)
- AddSimplex(X, s) : SmpCpx, SetEnum -> SmpCpx
- Prune(X, f) : SmpCpx, SetEnum -> SmpCpx
- Glue(X, e) : SmpCpx, SeqEnum -> SmpCpx
- Example SmpCpx_prune-glue (H149E11)
- 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 (H149E12)
- Standard Topological Objects
- Homology Computation
- Homology(X) : SmpCpx -> SeqEnum, SeqEnum
- Example SmpCpx_homology (H149E13)
- 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 (H149E14)
- HomologyGenerators(X) : SmpCpx ->
- Example SmpCpx_homologygenerators (H149E15)
- Bibliography
V2.28, 13 July 2023