divisorPoset(RingElement,RingElement) -- generates the poset of divisors with a lower and upper bound

i1 : R = QQ[x,y];

i2 : divisorPoset(x*y-x, x^2*y^2 - 2*x^2*y + x^2)

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

o2 : Poset