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 object of class 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 = Poset{cache => CacheTable{}                                                                                                                                                                                    }
                                2                2                 2         2
           GroundSet => {ideal(x  - y*Z), ideal(y  - z*Z), ideal (y  - z*Z, x  - y*Z)}
           RelationMatrix => | 1 0 1 |
                             | 0 1 1 |
                             | 0 0 1 |
                                 2                2                  2                 2         2                  2                 2         2                   2         2                 2         2
           Relations => {{ideal(y  - z*Z), ideal(y  - z*Z)}, {ideal(x  - y*Z), ideal (y  - z*Z, x  - y*Z)}, {ideal(y  - z*Z), ideal (y  - z*Z, x  - y*Z)}, {ideal (y  - z*Z, x  - y*Z), ideal (y  - z*Z, x  - y*Z)}}

o2 : Poset

Caveat

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

Ways to use `projectivizeArrangement` :

projectivizeArrangement(List,Ring)

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

Synopsis

Description

Caveat

See also

Ways to use projectivizeArrangement :

Ways to use `projectivizeArrangement` :