simplicialChainComplex -- the non-reduced homological chain complex that is determined by an abstract simplicial complex

Usage:

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

Description

This method returns the (non-reduced) homological chain complex (i.e., there is no nonzero term in homological degree $-1$ that corresponds to the empty face) that is associated to an abstract simplicial complex. The chain complex is defined over the integers.

i1 : K = abstractSimplicialComplex({{1,2,3},{1,4,5},{2,4,5,7}})

o1 = AbstractSimplicialComplex{-1 => {{}}                                                                                   }
                               0 => {{1}, {2}, {3}, {4}, {5}, {7}}
                               1 => {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {2, 7}, {4, 5}, {4, 7}, {5, 7}}
                               2 => {{1, 2, 3}, {1, 4, 5}, {2, 4, 5}, {2, 4, 7}, {2, 5, 7}, {4, 5, 7}}
                               3 => {{2, 4, 5, 7}}

o1 : AbstractSimplicialComplex

i2 : C = simplicialChainComplex(K)

       6       11       6       1
o2 = ZZ  <-- ZZ   <-- ZZ  <-- ZZ
                               
     0       1        2       3

o2 : Complex

Ways to use simplicialChainComplex:

simplicialChainComplex(AbstractSimplicialComplex)

For the programmer

The object simplicialChainComplex is a method function.

The source of this document is in AbstractSimplicialComplexes.m2:864:0.