If an abstract simplicial complex can be regarded as a subsimplicial complex of another abstract simplicial complex, then it is useful to calculate the induced map at the level of Reduced Simplicial Chain Complexes. This is made possible by the method inducedReducedSimplicialChainComplexMap.
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
|
i3 : inducedReducedSimplicialChainComplexMap(J,K)
1 1
o3 = -1 : ZZ <--------- ZZ : -1
| 1 |
3 3
0 : ZZ <------------- ZZ : 0
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
3 1
1 : ZZ <--------- ZZ : 1
| 1 |
| 0 |
| 0 |
o3 : ComplexMap
|
i4 : L = abstractSimplicialComplex {{}}
o4 = AbstractSimplicialComplex{-1 => {{}}}
o4 : AbstractSimplicialComplex
|
i5 : inducedReducedSimplicialChainComplexMap(L,L)
o5 = -2 : 0 <----- 0 : -2
0
1 1
-1 : ZZ <--------- ZZ : -1
| 1 |
o5 : ComplexMap
|
i6 : M = abstractSimplicialComplex {{1}}
o6 = AbstractSimplicialComplex{-1 => {{}}}
0 => {{1}}
o6 : AbstractSimplicialComplex
|
i7 : L = abstractSimplicialComplex {{}}
o7 = AbstractSimplicialComplex{-1 => {{}}}
o7 : AbstractSimplicialComplex
|
i8 : inducedReducedSimplicialChainComplexMap(M,L)
o8 = -2 : 0 <----- 0 : -2
0
1 1
-1 : ZZ <--------- ZZ : -1
| 1 |
o8 : ComplexMap
|