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

## Synopsis

• Usage:
P = projectivizeArrangement(L, R)
• Inputs:
• L, a list, which gives the equations defining the (possibly non-projective) hyperplane arrangement
• R, a ring, which the hyperplanes are defined over
• Outputs:
• P, an instance of the type Poset,

## Description

This method returns the intersectionLattice of the projectivization of the specified hyperplane arrangement.

 i1 : R = QQ[x,y,z]; i2 : projectivizeArrangement({x^2-y, y^2-z}, R) o2 = Relation Matrix: | 1 0 1 0 | | 0 1 1 0 | | 0 0 1 0 | | 1 1 1 1 | o2 : Poset

## Caveat

The variable used for homogenization is $Z$, and so the ring $R$ should not already have this variable in use.