# 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

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