# DeltaComplex VS¶

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:

=: (%, %) -> Boolean

from BasicType

~=: (%, %) -> Boolean

from BasicType

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
coHomology: % -> List Homology

calculate cohomology using SmithNormalForm

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.

homology: % -> List Homology

calculate homology using SmithNormalForm

latex: % -> String

from SetCategory

a simplicial complex with one link

oneSkeleton: % -> UndirectedGraph NonNegativeInteger

generates graph AKA 1-skeleton

triangle: (NonNegativeInteger, NonNegativeInteger, NonNegativeInteger) -> %

a simplicial complex with one triangle

BasicType

SetCategory