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

The following code is a slight modification of the code to find the 16 possible betti tables. Simply go thru all the tables, but only resolve the quadratic terms.

 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| | | +--------------+--------------+--------------+----------------+