The function produces the shape of the matrix factorization induced by a module with Betti table B on a hypersurface of degree d, assuming that all the possible cancellations occur
i1 : p=32009; |
i2 : Fp=ZZ/p; |
i3 : S=Fp[x_0..x_4]; |
i4 : beta=betti map(S^{12:0,1:-1},S^{1:-1,12:-2},0) 0 1 o4 = total: 13 13 0: 12 1 1: 1 12 o4 : BettiTally |
i5 : d=3; |
i6 : L=candidateTables(beta,3) 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 o6 = {total: 1 7 10 6 2, total: 2 8 9 5 2, total: 1 5 11 8 1, total: 3 7 9 6 0: 1 . . . . 0: 1 1 . . . 0: 1 . . . . 1: 3 7 1 . 1: . 7 9 1 . 1: 1 7 9 . . 1: . 4 . . . 2: . . 8 5 2: . . 1 5 2 2: . . . 5 2 2: . 1 11 8 . 3: . . . 1 3: . . . . 1 ------------------------------------------------------------------------ 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 1, total: 2 9 10 4 1, total: 2 6 10 7 1, total: 3 7 9 6 1, total: 2 9 10 . 0: 1 . . . . 0: 1 . . . . 1: 3 6 . . . 0: 2 1 . . 1: 1 9 10 1 . 1: 1 6 . . . 2: . 1 9 6 1 1: . 8 9 1 2: . . . 3 1 2: . . 10 6 . 2: . . 1 3: . . . 1 1 ------------------------------------------------------------------------ 3 4 0 1 2 3 4 0 1 2 3 0 1 2 3 0 1 2 4 1, total: 4 8 8 5 1, total: 4 9 9 4, total: 2 10 11 3, total: 3 11 10 . . 1: 4 8 . . . 1: 4 8 1 . 0: 2 . . . 0: 2 1 . . . 2: . . 8 4 1 2: . 1 8 4 1: . 10 10 1 1: 1 10 10 4 1 3: . . . 1 . 2: . . 1 2 2: . . . ------------------------------------------------------------------------ 3 0 1 2 3 0 1 2 3 0 1 2 3 2, total: 3 8 10 5, total: 5 10 8 3, total: 4 9 9 4} . 0: 1 . . . 1: 5 10 1 . 0: 1 . . . . 1: 2 7 . . 2: . . 7 2 1: 3 9 . . 2 2: . 1 10 5 3: . . . 1 2: . . 9 3 3: . . . 1 o6 : List |
i7 : apply(L,l->arisingMatFac(l,d)) 0 1 0 1 0 1 0 1 0 1 o7 = {total: 13 13, total: 13 13, total: 12 12, total: 12 12, total: 13 13, 0: 1 . 0: 1 . 0: 12 . 0: 12 . 0: 1 . 1: 12 12 1: 12 12 1: . 12 1: . 12 1: 12 12 2: . 1 2: . 1 2: . 1 ------------------------------------------------------------------------ 0 1 0 1 0 1 0 1 0 1 total: 12 12, total: 13 13, total: 12 12, total: 13 13, total: 13 13, 0: 12 . 0: 12 1 0: 12 12 0: 12 1 0: 12 1 1: . 12 1: 1 12 1: 1 12 1: 1 12 ------------------------------------------------------------------------ 0 1 0 1 0 1 0 1 0 1 total: 13 13, total: 13 13, total: 12 12, total: 12 12, total: 12 12} 0: 1 . 0: 1 . 0: 12 . 0: 12 . 0: 12 . 1: 12 12 1: 12 12 1: . 12 1: . 12 1: . 12 2: . 1 2: . 1 o7 : List |