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Posets :: projectivizeArrangement

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.

See also

intersectionLattice -- generates the intersection lattice of a hyperplane arrangement

Ways to use `projectivizeArrangement` :

"projectivizeArrangement(List,Ring)"

For the programmer

The object projectivizeArrangement is a method function.