How to make subsimplical complexes and induced simplicial chain complex maps -- Induced simplicial chain complex maps via subsimplicial complexes

i1 : K = abstractSimplicialComplex(4,3)

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}}

o1 : AbstractSimplicialComplex

i2 : L = abstractSimplicialComplex(4,2)

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

o2 : AbstractSimplicialComplex

i3 : f = inducedSimplicialChainComplexMap(K,L)

           4                    4
o3 = 0 : ZZ  <--------------- ZZ  : 0
                | 1 0 0 0 |
                | 0 1 0 0 |
                | 0 0 1 0 |
                | 0 0 0 1 |

           6                        6
     1 : ZZ  <------------------- ZZ  : 1
                | 1 0 0 0 0 0 |
                | 0 1 0 0 0 0 |
                | 0 0 1 0 0 0 |
                | 0 0 0 1 0 0 |
                | 0 0 0 0 1 0 |
                | 0 0 0 0 0 1 |

o3 : ComplexMap

i4 : isWellDefined f

o4 = true

i5 : fRed = inducedReducedSimplicialChainComplexMap(K,L)

            1              1
o5 = -1 : ZZ  <--------- ZZ  : -1
                 | 1 |

           4                    4
     0 : ZZ  <--------------- ZZ  : 0
                | 1 0 0 0 |
                | 0 1 0 0 |
                | 0 0 1 0 |
                | 0 0 0 1 |

           6                        6
     1 : ZZ  <------------------- ZZ  : 1
                | 1 0 0 0 0 0 |
                | 0 1 0 0 0 0 |
                | 0 0 1 0 0 0 |
                | 0 0 0 1 0 0 |
                | 0 0 0 0 1 0 |
                | 0 0 0 0 0 1 |

o5 : ComplexMap

i6 : isWellDefined fRed

o6 = true