HH_ZZ SimplicialComplex -- Compute the homology of a simplicial complex.

Synopsis

• Function: homology

• Usage:

  homology(j,C)

• Inputs:
  • j, an integer
  • C, a simplicial complex
• Outputs:
  • a module

Description

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)

o3 = cokernel | 2 |

                              1
o3 : ZZ-module, quotient of ZZ

See also

• HH_ZZ(SimplicialComplex,Ring) -- Compute the homology of a simplicial complex.
• boundary -- boundary operator
• chainComplex(SimplicialComplex) -- The chain complex of boundary maps.