If (phi,psi) is a matrix factorization, then also (dual psi, dual phi), (psi, syz psi), and (dual phi, syz dual phi) are. This function provides a list of the shapes of the above matrix factorizations, including the original one
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 |
i5 : listOfPossibleMatFac(beta,3) 0 1 0 1 o5 = {total: 10 10, total: 10 10} 0: 9 1 0: 1 . 1: 1 9 1: 9 9 2: . 1 o5 : List |
i6 : listOfPossibleMatFac(beta,4) 0 1 0 1 o6 = {total: 10 10, total: 10 10} 0: 9 1 0: 1 . 1: 1 9 1: 9 . 2: . 9 3: . 1 o6 : List |
i7 : beta=betti map(S^{9:0,1:-1},S^{0:-1,10:-2},0) 0 1 o7 = total: 10 10 0: 9 . 1: 1 10 o7 : BettiTally |
i8 : listOfPossibleMatFac(beta,3) 0 1 0 1 0 1 0 1 o8 = {total: 10 10, total: 10 10, total: 10 10, total: 10 10} 0: 9 . 0: 10 1 0: 10 9 0: 1 . 1: 1 10 1: . 9 1: . 1 1: 9 10 o8 : List |