-- -*- M2-comint -*- {* hash: -1496335151 *}

i1 : S = QQ[a,b,c,d];

i2 : I = ideal (b^2-a*d, a*d-b*c, c^2-b*d);

o2 : Ideal of S

i3 : M = monomialIdeal (b^2, b*c, c^2);

o3 : MonomialIdeal of S

i4 : L = lcmLattice (I);

i5 : L.GroundSet

       2                      2           3       2               2 2   2 2  
o5 = {b  - a*d, - b*c + a*d, c  - b*d, - b c + a*b d + a*b*c*d - a d , b c  -
     ------------------------------------------------------------------------
      3       2         2       3    2         2         2     3 3    4     
     b d - a*c d + a*b*d , - b*c  + b c*d + a*c d - a*b*d , - b c  + b c*d +
     ------------------------------------------------------------------------
        2 2         3       3 2      2   2    2 2 2    2   3
     a*b c d + a*b*c d - a*b d  - a*b c*d  - a c d  + a b*d }

o5 : List

i6 : L.RelationMatrix

o6 = | 1 0 0 1 1 0 1 |
     | 0 1 0 1 0 1 1 |
     | 0 0 1 0 1 1 1 |
     | 0 0 0 1 0 0 1 |
     | 0 0 0 0 1 0 1 |
     | 0 0 0 0 0 1 1 |
     | 0 0 0 0 0 0 1 |

              7        7
o6 : Matrix ZZ  <--- ZZ

i7 : LM = lcmLattice (M);

i8 : LM.GroundSet

       2        2   2    2 2     2
o8 = {b , b*c, c , b c, b c , b*c }

o8 : List

i9 : LM.RelationMatrix

o9 = | 1 0 0 1 1 0 |
     | 0 1 0 1 1 1 |
     | 0 0 1 0 1 1 |
     | 0 0 0 1 1 0 |
     | 0 0 0 0 1 0 |
     | 0 0 0 0 1 1 |

              6        6
o9 : Matrix ZZ  <--- ZZ

i10 :