divisorPoset(RingElement) -- generates the poset of divisors

i1 : R = QQ[x,y];

i2 : divisorPoset(x^2*y)

o2 = Poset{cache => CacheTable{...6...}                                                     }
                                        2   2
           GroundSet => {1, y, x, x*y, x , x y}
           RelationMatrix => | 1 1 1 1 1 1 |
                             | 0 1 0 1 0 1 |
                             | 0 0 1 1 1 1 |
                             | 0 0 0 1 0 1 |
                             | 0 0 0 0 1 1 |
                             | 0 0 0 0 0 1 |
                                                                  2          2      2   2
           Relations => {{1, y}, {1, x}, {y, x*y}, {x, x*y}, {x, x }, {x*y, x y}, {x , x y}}

o2 : Poset

i3 : divisorPoset(x*y^2 - 2*x*y + x)

o3 = Poset{cache => CacheTable{...6...}                                                                                                                       }
                                       2                       2
           GroundSet => {1, y - 1, x, y  - 2y + 1, x*y - x, x*y  - 2x*y + x}
           RelationMatrix => | 1 1 1 1 1 1 |
                             | 0 1 0 1 1 1 |
                             | 0 0 1 0 1 1 |
                             | 0 0 0 1 0 1 |
                             | 0 0 0 0 1 1 |
                             | 0 0 0 0 0 1 |
                                                      2                                              2              2                           2
           Relations => {{1, y - 1}, {1, x}, {y - 1, y  - 2y + 1}, {y - 1, x*y - x}, {x, x*y - x}, {y  - 2y + 1, x*y  - 2x*y + x}, {x*y - x, x*y  - 2x*y + x}}

o3 : Poset