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Posets :: intersectionLattice

intersectionLattice -- generates the intersection lattice of a hyperplane arrangement

Synopsis

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 = Poset{cache => CacheTable{}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    }
           GroundSet => {ideal(x + y), ideal(x + z), ideal (y - z, x + z), ideal(y + z), ideal (y + z, x - z), ideal (y + z, x + z), ideal (z, y, x)}
           RelationMatrix => | 1 0 1 0 1 0 1 |
                             | 0 1 1 0 0 1 1 |
                             | 0 0 1 0 0 0 1 |
                             | 0 0 0 1 1 1 1 |
                             | 0 0 0 0 1 0 1 |
                             | 0 0 0 0 0 1 1 |
                             | 0 0 0 0 0 0 1 |
           Relations => {{ideal(x + z), ideal(x + z)}, {ideal(x + y), ideal (y - z, x + z)}, {ideal(x + z), ideal (y - z, x + z)}, {ideal (y - z, x + z), ideal (y - z, x + z)}, {ideal(y + z), ideal(y + z)}, {ideal(x + y), ideal (y + z, x - z)}, {ideal(y + z), ideal (y + z, x - z)}, {ideal (y + z, x - z), ideal (y + z, x - z)}, {ideal(x + z), ideal (y + z, x + z)}, {ideal(y + z), ideal (y + z, x + z)}, {ideal (y + z, x + z), ideal (y + z, x + z)}, {ideal(x + y), ideal (z, y, x)}, {ideal(x + z), ideal (z, y, x)}, {ideal (y - z, x + z), ideal (z, y, x)}, {ideal(y + z), ideal (z, y, x)}, {ideal (y + z, x - z), ideal (z, y, x)}, {ideal (y + z, x + z), ideal (z, y, x)}, {ideal (z, y, x), ideal (z, y, x)}}

o2 : Poset

See also

Ways to use intersectionLattice :