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: . . ------------------------------------------------------------------------ 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 |