HH_ZZ(SimplicialComplex,Ring) -- Compute the homology of a simplicial complex.

i1 : R=ZZ[x_0..x_5];

i2 : D=simplicialComplex apply({{x_0, x_1, x_2}, {x_1, x_2, x_3}, {x_0, x_1, x_4}, {x_0, x_3, x_4}, {x_2, x_3, x_4}, {x_0, x_2, x_5}, {x_0, x_3, x_5}, {x_1, x_3, x_5}, {x_1, x_4, x_5}, {x_2, x_4, x_5}},face)

o2 = | x_2x_4x_5 x_1x_4x_5 x_1x_3x_5 x_0x_3x_5 x_0x_2x_5 x_2x_3x_4 x_0x_3x_4 x_0x_1x_4 x_1x_2x_3 x_0x_1x_2 |

o2 : SimplicialComplex

i3 : prune homology(1,D,ZZ)

o3 = cokernel | 2 |

                              1
o3 : ZZ-module, quotient of ZZ

i4 : prune homology(1,D,QQ)

o4 = 0

o4 : QQ-module

i5 : prune homology(1,D,ZZ/2)

      ZZ 1
o5 = (--)
       2

     ZZ
o5 : ---module, free
      2