# DeltaComplex VSΒΆ

- VS: AbelianGroup

Similar to Simplicial Complex but faces (edges, triangles, etc.) are indexed by ‘face maps’ into the next lower face map until we get down to the vertices. for more documentation see: http://www.euclideanspace.com/prog/scratchpad/mycode/topology/delta/ Date Created: Feb 2016 Basic Operations: Related packages: Related categories: Related Domains: FiniteSimplicialComplex is a simpler and more compact representation which can be used if edges, triangles, etc. don`'t`

need to be indexed. Also See: AMS Classifications:

- chain: % -> ChainComplex
- returns a matrix sequence representing the face maps in linear algebra form

- coChain: % -> CoChainComplex VS
- returns a matrix sequence representing the face maps in linear algebra form

- coerce: % -> FiniteSimplicialComplex VS
`coerce DeltaComplex`

to FiniteSimplicialComplex- coerce: % -> OutputForm
- from CoercibleTo OutputForm

deltaComplex: (FiniteSimplicialComplex VS, Boolean) -> %

- deltaComplex: (List VS, NonNegativeInteger, List List List Integer) -> %
- constructor where the simplices are supplied

- deltaComplex: FiniteCubicalComplex VS -> %
- construct from FiniteCubicalComplex. This builds indexes of edges, squares and so on.

- deltaComplex: FiniteSimplicialComplex VS -> %
- construct from FiniteSimplicialComplex. This builds indexes of edges, triangles and so on.

- faceMap: (%, NonNegativeInteger) -> List List Integer
- returns an individual face map specified by
`n`

. Where`'n'`

is the dimension required, so`n=1`

returns one dimentional faces (edges),`n=2`

returns two dimentional faces (triamgles), and so on. used by fundamentalGroup.

- fundamentalGroup: % -> GroupPresentation
- Generates fundamental group from this simplicial complex.

- fundamentalGroup: (%, Boolean, Boolean) -> GroupPresentation
- Generates fundamental group from this simplicial complex.
- hash: % -> SingleInteger
- from SetCategory
- hashUpdate!: (HashState, %) -> HashState
- from SetCategory

- homology: % -> List Homology
- calculate homology using SmithNormalForm
- latex: % -> String
- from SetCategory

- link: (NonNegativeInteger, NonNegativeInteger) -> %
- a simplical complex with one link

- oneSkeleton: % -> UndirectedGraph NonNegativeInteger
- generates graph AKA 1-skeleton

- triangle: (NonNegativeInteger, NonNegativeInteger, NonNegativeInteger) -> %
- a simplical complex with one triangle