DeltaComplex VSΒΆ

alg_top.spad line 2924

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
from CoercibleTo 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 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

BasicType

CoercibleTo OutputForm

SetCategory