intersectionLattice -- generates the intersection lattice of a hyperplane arrangement

Synopsis

• Usage:

  P = intersectionLattice(L, R)

• Inputs:
  • L, a list, which gives the equations defining the hyperplane arrangement
  • R, a ring, which the hyperplanes are defined over
• Outputs:
  • P, an instance of the type Poset,

Description

i1 : R = QQ[x,y,z];

i2 : intersectionLattice({x+y, x+z, y+z}, R)

o2 = Relation Matrix: | 1 0 1 0 1 0 1 0 |
                      | 0 1 1 0 0 1 1 0 |
                      | 0 0 1 0 0 0 1 0 |
                      | 0 0 0 1 1 1 1 0 |
                      | 0 0 0 0 1 0 1 0 |
                      | 0 0 0 0 0 1 1 0 |
                      | 0 0 0 0 0 0 1 0 |
                      | 1 1 1 1 1 1 1 1 |

o2 : Poset

See also

• projectivizeArrangement -- computes the intersection poset of a projectivized hyperplane arrangement