-- -*- M2-comint -*- {* hash: 2114582415 *}

i1 : G = {a,b,c,d};

i2 : R = {(a,b), (a,c), (c,d)};

i3 : P = poset (G,R)

o3 = Poset{cache => CacheTable                  }
           GroundSet => {a, b, c, d}
           RelationMatrix => | 1 1 1 1 |
                             | 0 1 0 0 |
                             | 0 0 1 1 |
                             | 0 0 0 1 |
           Relations => {(a, b), (a, c), (c, d)}

o3 : Poset

i4 : S = QQ[x,y,z];

i5 : G = {x^2, x*y, z^2, x^2*y*z, x*y*z^3, x^2*y^2*z^3};

i6 : R = select((flatten apply (G, g-> apply (G, h-> if h % g == 0 then (g,h)))), i -> i =!= null) -- finds all pairs where g divides h

        2   2     2   2        2   2 2 3                      2           
o6 = {(x , x ), (x , x y*z), (x , x y z ), (x*y, x*y), (x*y, x y*z), (x*y,
     ------------------------------------------------------------------------
          3          2 2 3     2   2     2       3     2   2 2 3     2    
     x*y*z ), (x*y, x y z ), (z , z ), (z , x*y*z ), (z , x y z ), (x y*z,
     ------------------------------------------------------------------------
      2        2      2 2 3         3       3         3   2 2 3     2 2 3 
     x y*z), (x y*z, x y z ), (x*y*z , x*y*z ), (x*y*z , x y z ), (x y z ,
     ------------------------------------------------------------------------
      2 2 3
     x y z )}

o6 : List

i7 : M = matrix apply (G, g-> apply (G, h-> if h % g == 0 then 1 else 0))

o7 = | 1 0 0 1 0 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 |

              6        6
o7 : Matrix ZZ  <--- ZZ

i8 : P = poset(G,R,M)

o8 = Poset{cache => CacheTable                                                                                                                                                                                                                    }
                          2        2   2          3   2 2 3
           GroundSet => {x , x*y, z , x y*z, x*y*z , x y z }
           RelationMatrix => | 1 0 0 1 0 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        2   2 2 3                      2                 3          2 2 3     2   2     2       3     2   2 2 3     2      2        2      2 2 3         3       3         3   2 2 3     2 2 3   2 2 3
           Relations => {(x , x ), (x , x y*z), (x , x y z ), (x*y, x*y), (x*y, x y*z), (x*y, x*y*z ), (x*y, x y z ), (z , z ), (z , x*y*z ), (z , x y z ), (x y*z, x y*z), (x y*z, x y z ), (x*y*z , x*y*z ), (x*y*z , x y z ), (x y z , x y z )}

o8 : Poset

i9 :