Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Taggar`SimplicialHomology`
SimplicialComplex  |
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automatically adds the closure of the supplied simplices.
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[…]["FVector"] returns where denotes the number of -dimensional simplices.
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"Dimension" | dimension of the simplicial complex | |
"Simplices" | association of all simplices that constitute the simplicial complex | |
"SimplexCount" | number of all simplices that constitute the simplicial complex | |
"EulerCharacteristic" | Euler characteristic of the simplicial complex | |
"Vertices" | list of all 0-simplices in the simplicial complex | |
"VertexCount" | number of 0-simplices in the simplicial complex | |
"Edges" | list of all 1-simplices in the simplicial complex | |
"EdgeCount" | number of 1-simplices in the simplicial complex | |
"Facets" | list of maximal simplices in the simplicial complex | |
"FacetCount" | number of maximal simplices in the simplicial complex | |
"FVector" | f-vector of the simplicial complex | |
"PureQ" | whether the simplicial complex is pure or not | |
"1Skeleton" | graph object representing the 1-skeleton of the simplicial complex | |
"ConnectedComponents" | connected components of the simplicial complex | |
"ConnectedQ" | whether the simplicial complex is connected or not | |
"Properties" | list of all properties |
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Simplicial complexes can be created using named objects, of which the following are accepted:
{"Simplex", n | n | |
"Point" | point (0-dimensional simplex) | |
"Line" | line (1-dimensional simplex) | |
"Triangle" | triangle (2-dimensional simplex) | |
"Tetrahedron" | tetrahedron (3-dimensional simplex) | |
{"Circle", n | n | |
"Circle" | circle (1-dimensional circle) | |
"Sphere" | sphere (2-dimensional circle) | |
{"CircleWedge", n | wedge product of n | |
"Torus" | 1-holed torus | |
"KleinBottle" | Klein bottle | |
"MobiusStrip" | Mobius strip | |
"RealProjectivePlane" | real projective plane | |
"ComplexProjectivePlane" | complex projective plane | |
"DunceHat" | dunce hat given by Hachimori (2016) | |
"PoincareHomologyThreeSphere" | Poincaré homology 3-sphere | |
"RudinBall" | non-shellable ball constructed by Rudin | |
"ZieglerBall" | non-shellable ball constructed by Ziegler |
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supports the following options:
"MaximalityCheck"  | checks whether provided facets are maximal |
Examples
(14)
Basic Examples
(6)
Construct various simplicial complexes such as the point:
In[1]:=
 | SimplicialComplex |
Out[1]=
SimplicialComplex
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Click on "+" to see more information about this simplicial complex. Or obtain information about the simplicial complex using some of its properties:
In[2]:=
%["Dimension"]%%["Simplices"]%%%["EulerCharacteristic"]
Out[2]=
0
Out[2]=
0{{1}}
Out[2]=
1
Construct the line segment :
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1
In[1]:=
| SimplicialComplex |
Out[1]=
SimplicialComplex
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Two disjoint points :
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In[1]:=
| SimplicialComplex |
Out[1]=
SimplicialComplex
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S
1
In[1]:=
| SimplicialComplex |
Out[1]=
SimplicialComplex
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D
2
In[1]:=
| SimplicialComplex |
Out[1]=
SimplicialComplex
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A simplicial complex created from two disjoint simplices is not connected:
In[1]:=
 | SimplicialComplex |
Out[1]=
False
Scope
(5)
Options
(1)
Properties & Relations
(2)
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