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abstractSimplicialComplex -- The abstractSimplicialComplex that is determined by an abstract simplicial complex

Description

This method returns the AbstractSimplicialComplex that represents a given abstract simplicial complex. The input is either a given collection of generating faces or an integer. These facets need not be facets. Moreover, the elements of the faces need not be written in lexiographic order. When the input is an integer, the output is the corresponding simplex.

i1 : abstractSimplicialComplex({{1,2,3,4}})

o1 = AbstractSimplicialComplex{-1 => {{}}                                           }
                               0 => {{1}, {2}, {3}, {4}}
                               1 => {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}}
                               2 => {{1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}}
                               3 => {{1, 2, 3, 4}}

o1 : AbstractSimplicialComplex
 
i2 : abstractSimplicialComplex({{4,1,2,3}, {3,2,5},{1,5}})

o2 = AbstractSimplicialComplex{-1 => {{}}                                                                   }
                               0 => {{1}, {2}, {3}, {4}, {5}}
                               1 => {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {3, 4}, {3, 5}}
                               2 => {{1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {2, 3, 5}}
                               3 => {{1, 2, 3, 4}}

o2 : AbstractSimplicialComplex
 
i3 : abstractSimplicialComplex(4)

o3 = AbstractSimplicialComplex{-1 => {{}}                                           }
                               0 => {{1}, {2}, {3}, {4}}
                               1 => {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}}
                               2 => {{1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}}
                               3 => {{1, 2, 3, 4}}

o3 : AbstractSimplicialComplex

The simplicial complex on [n] with r-skelton can be constructed as follows.

i4 : abstractSimplicialComplex(4,2)

o4 = AbstractSimplicialComplex{-1 => {{}}                                           }
                               0 => {{1}, {2}, {3}, {4}}
                               1 => {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}}

o4 : AbstractSimplicialComplex

Ways to use abstractSimplicialComplex:

For the programmer

The object abstractSimplicialComplex is a method function.