Simplicial Complexes
SimplicialComplex(f) : SeqEnum[SetEnum] -> SmpCpx
Example SmpCpx_construct (H140E1)
SimplicialComplex(G) : Grph -> SmpCpx
FlagComplex(G) : Grph -> SmpCpx
Dimension(X) : SmpCpx -> RngIntelt
Example SmpCpx_dimension (H140E2)
Faces(X, d) : SmpCpx, RngIntElt -> SeqEnum[SetEnum]
Example SmpCpx_faces (H140E3)
Facets(X) : SmpCpx -> SeqEnum[SetEnum]
Example SmpCpx_facets (H140E4)
Normalization(X) : SmpCpx -> SmpCpx
Shift(X, n) : SmpCpx, RngIntelt -> SmpCpx
Example SmpCpx_normalize-shift (H140E5)
Boundary(X) : SmpCpx -> SmpCpx
Example SmpCpx_boundary (H140E6)
S + T : SmpCpx, SmpCpx -> SmpCpx
Example SmpCpx_sum (H140E7)
S eq T : SmpCpx, SmpCpx -> BoolElt
Example SmpCpx_eq (H140E8)
Product(S,T) : SmpCpx, SmpCpx -> SmpCpx
Example SmpCpx_product (H140E9)
Join(S,T) : SmpCpx, SmpCpx -> SmpCpx
Example SmpCpx_join (H140E10)
AddSimplex(X, s) : SmpCpx, SetEnum -> SmpCpx
Prune(X, f) : SmpCpx, SetEnum -> SmpCpx
Glue(X, e) : SmpCpx, SeqEnum -> SmpCpx
Example SmpCpx_prune-glue (H140E11)
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 (H140E12)
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 (H140E13)
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 (H140E14)
HomologyGenerators(X) : SmpCpx ->
Example SmpCpx_homologygenerators (H140E15)
Bibliography
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Version: V2.19 of
Wed Apr 24 15:09:57 EST 2013