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# intersectionLattice -- generates the intersection lattice of a hyperplane arrangement

- 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

The intersection lattice of a hyperplane arrangement is the lattice of intersections in the arrangement partially ordered by containment.

    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

## Ways to use intersectionLattice:

- `intersectionLattice(List,Ring)`

## For the programmer

The object intersectionLattice is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Posets.m2:3570:0.