Given the shape of the desired matrix facorization, we compute a list of hypothetical resolutions, which could lead to such a matrix factorization, as all integral points in the Boij-Soederberg cone.
i1 : kk=ZZ/10007;S=kk[x_0..x_4]; |
i3 : beta=betti random(S^3,S^{3:-1})
0 1
o3 = total: 3 3
0: 3 3
o3 : BettiTally
|
i4 : BSCandidates(beta,3)
0 1 2 3 0 1 2 0 1
o4 = {total: 1 2 2 1, total: 2 3 1, total: 3 3}
0: 1 2 . . 0: 2 3 . 0: 3 3
1: . . 2 1 1: . . 1
o4 : List
|
i5 : beta=betti random(S^9,S^{9:-1})
0 1
o5 = total: 9 9
0: 9 9
o5 : BettiTally
|
i6 : cands=BSCandidates(beta,3)
0 1 2 3 0 1 2 3 0 1 2 3 0 1 0 1
o6 = {total: 3 6 6 3, total: 4 7 5 2, total: 5 7 4 2, total: 9 9, total: 7 9
0: 3 6 . . 0: 4 7 . . 0: 5 7 . . 0: 9 9 0: 7 9
1: . . 6 3 1: . . 5 2 1: . . 4 2 1: . .
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2 0 1 2 0 1 2 0 1 2 3 0 1 2 3 0
2, total: 6 9 3, total: 8 9 1, total: 7 8 2 1, total: 5 8 4 1, total: 6
. 0: 6 9 . 0: 8 9 . 0: 7 8 . . 0: 5 8 . . 0: 6
2 1: . . 3 1: . . 1 1: . . 2 1 1: . . 4 1 1: .
------------------------------------------------------------------------
1 2 3
8 3 1}
8 . .
. 3 1
o6 : List
|
i7 : apply(select(cands,b->codim b>2),b->(codim b,degree b, betti b))
0 1 2 3
o7 = {(3, 6, total: 3 6 6 3)}
0: 3 6 . .
1: . . 6 3
o7 : List
|