ambientAbstractSimplicialComplex -- the ambient simplex

Usage:

ambientAbstractSimplicialComplex(K)
Inputs:
- K, an abstract simplicial complex,
Outputs:
- an abstract simplicial complex,

Description

If an abstract simplicial complex has vertices supported on a subset of $[n] = \{1,\dots,n\}$, and including $n$, then it seems useful to regard this simplicial complex as being a subsimplicial complex of the simplex on $[n]$. This method returns this simplex as the ambient simplicial complex.

i1 : K = abstractSimplicialComplex({{1,2},{3}})

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

o1 : AbstractSimplicialComplex

i2 : J = ambientAbstractSimplicialComplex(K)

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

o2 : AbstractSimplicialComplex

Ways to use ambientAbstractSimplicialComplex:

ambientAbstractSimplicialComplex(AbstractSimplicialComplex)

For the programmer

The object ambientAbstractSimplicialComplex is a method function.

The source of this document is in AbstractSimplicialComplexes.m2:733:0.