# DeltaComplex VS¶

alg_top.spad line 2898 [edit on github]

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 dimensional faces (edges),`n=2`

returns two dimensional 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.

- latex: % -> String
from SetCategory

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

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

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