Finding all possible betti tables for quadratic component of inverse system for quartics in 4 variables -- Material from Section 4 of [QQ]

i1 : GetQuads = (d,k,n)->(
         R=ZZ/2[x_1..x_k];
         quartics=super basis(d,R);
         MonList=apply(rank source quartics, i->quartics_(0,i));
         L=subsets(MonList,n);
         J=apply(L, j->(F=gens ideal sum j;
         InvSysF=fromDual F;
         Idegs=degrees source mingens ideal InvSysF;
         if (not ((member({1},Idegs)))) then minimalBetti coker super basis(2, ideal InvSysF)));
         Jlist =drop(unique J,1);
         netList pack(4,Jlist))

o1 = GetQuads

o1 : FunctionClosure

i2 : GetQuads(4,4,2)

     +--------------+--------------+--------------+----------------+
     |       0 1 2 3|       0 1 2 3|       0 1 2 3|       0 1 2 3  |
o2 = |total: 1 6 8 3|total: 1 5 5 1|total: 1 4 4 1|total: 1 4 4 1  |
     |    0: 1 . . .|    0: 1 . . .|    0: 1 . . .|    0: 1 . . .  |
     |    1: . 6 8 3|    1: . 5 5 .|    1: . 4 3 .|    1: . 4 4 1  |
     |              |    2: . . . 1|    2: . . 1 1|                |
     +--------------+--------------+--------------+----------------+
     |       0 1 2 3|       0 1 2  |       0 1 2 3|       0 1 2 3 4|
     |total: 1 4 5 2|total: 1 3 2  |total: 1 3 3 1|total: 1 4 6 4 1|
     |    0: 1 . . .|    0: 1 . .  |    0: 1 . . .|    0: 1 . . . .|
     |    1: . 4 2 .|    1: . 3 2  |    1: . 3 . .|    1: . 4 . . .|
     |    2: . . 3 2|              |    2: . . 3 .|    2: . . 6 . .|
     |              |              |    3: . . . 1|    3: . . . 4 .|
     |              |              |              |    4: . . . . 1|
     +--------------+--------------+--------------+----------------+
     |       0 1 2  |       0 1 2 3|       0 1 2 3|                |
     |total: 1 2 1  |total: 1 5 6 2|total: 1 5 6 2|                |
     |    0: 1 . .  |    0: 1 . . .|    0: 1 . . .|                |
     |    1: . 2 .  |    1: . 5 5 1|    1: . 5 6 2|                |
     |    2: . . 1  |    2: . . 1 1|              |                |
     +--------------+--------------+--------------+----------------+