The function takes a random element f of minimal degree in the support of the annihilator of the module M (or in the ideal I) and produces the matrix factorization of f given by the periodic part of the R/f-resolution of M (or R/I)
i1 : S = ZZ/32009[x_0..x_3]; |
i2 : I = minors(3,random(S^4,S^{1:-1,2:-2}));
o2 : Ideal of S
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i3 : betti res I
0 1 2
o3 = total: 1 4 3
0: 1 . .
1: . . .
2: . . .
3: . . .
4: . 4 1
5: . . 2
o3 : BettiTally
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i4 : (phi, psi)=matrixFactorizationFromModule I; |
i5 : betti res ((S^1/I) ** (ring phi))
0 1 2 3 4 5
o5 = total: 1 4 4 3 3 3
0: 1 . . . . .
1: . . . . . .
2: . . . . . .
3: . . 1 . . .
4: . 4 1 . . .
5: . . 2 . . .
6: . . . . . .
7: . . . 3 1 .
8: . . . . 2 .
9: . . . . . .
10: . . . . . 3
o5 : BettiTally
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i6 : betti phi, betti psi
0 1 0 1
o6 = (total: 3 3, total: 3 3)
0: 3 1 1: 1 .
1: . 2 2: 2 .
3: . .
4: . 3
o6 : Sequence
|
i7 : SX = ring psi; |
i8 : phi*psi
o8 = 0
3 3
o8 : Matrix SX <--- SX
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