The function returns a list of possible Betti tables, lying in the Boij-Soederberg cone and whose support has codimension >= 3, with the additional assumption that their projective dimension is at most 4. A module having a Betti table belonging to this list leads to a matrix factorization (phi,psi), if no cancellation occurs, such that one among the matrix factorizations (dual psi, dual phi), (psi, syz psi), (dual phi, syz dual phi), or (phi, psi) itself, has shape B
i1 : p=32009; |
i2 : Fp=ZZ/p; |
i3 : S=Fp[x_0..x_4]; |
i4 : beta=betti map(S^{9:0,1:-1},S^{1:-1,9:-2},0)
0 1
o4 = total: 10 10
0: 9 1
1: 1 9
o4 : BettiTally
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i5 : d=3; |
i6 : time candidateTables(beta,d)
-- used 0.624644 seconds
0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4
o6 = {total: 1 6 8 4 1, total: 2 7 7 3 1, total: 1 4 8 6 1, total: 2 5 7 5 1,
0: 1 . . . . 0: 1 1 . . . 0: 1 . . . . 1: 2 4 . . .
1: . 6 7 1 . 1: 1 6 7 . . 1: . 4 . . . 2: . 1 7 5 1
2: . . 1 3 1 2: . . . 3 1 2: . . 8 5 .
3: . . . 1 1
------------------------------------------------------------------------
0 1 2 3 4 0 1 2 3 0 1 2 3 4 0 1 2 3
total: 1 5 7 5 2, total: 2 8 8 2, total: 2 5 7 5 1, total: 3 7 7 3,
0: 1 1 . . . 0: 1 . . . 1: 2 5 1 . . 1: 3 6 1 .
1: . 4 6 . . 1: 1 8 8 1 2: . . 6 4 . 2: . 1 6 3
2: . . 1 5 2 2: . . . 1 3: . . . 1 1
------------------------------------------------------------------------
0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
total: 2 8 8 2, total: 2 6 8 4, total: 4 8 6 2, total: 3 7 7 3}
0: 2 1 . . 0: 1 . . . 1: 4 8 1 . 0: 1 . . .
1: . 7 7 . 1: 1 5 . . 2: . . 5 1 1: 2 7 . .
2: . . 1 2 2: . 1 8 4 3: . . . 1 2: . . 7 2
3: . . . 1
o6 : List
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