DeltaComplex(VS)

alg_top.spad line 2909 [edit on github]

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
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

coHomology : % -> List(Homology)

calculate cohomology using SmithNormalForm

coerce : % -> FiniteSimplicialComplex(VS)

coerce DeltaComplex to FiniteSimplicialComplex

coerce : % -> OutputForm
from CoercibleTo(OutputForm)
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.

deltaComplex : (FiniteSimplicialComplex(VS), Boolean) -> %

deltaComplex : (List(VS), NonNegativeInteger, List(List(List(Integer)))) -> %

constructor where the simplices are supplied

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
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

~= : (%, %) -> Boolean
from BasicType

CoercibleTo(OutputForm)

SetCategory

BasicType