Given a module N over the coordinate ring S of P4 which is annihilated by a cubic f, the function returns the matrix of f obtained from the eventual periodic resolution of N as an S/f module.
i1 : kk=ZZ/10007;S=kk[x_0..x_4]; |
i3 : N=constructEx1(S); |
i4 : betti res N
0 1 2 3
o4 = total: 6 13 12 5
0: 6 13 3 .
1: . . 9 5
o4 : BettiTally
|
i5 : (M0,M1) = matrixFactorizationFromModule(N); |
i6 : betti M0, betti M1
0 1 0 1
o6 = (total: 18 18, total: 18 18)
-1: 3 . 1: 18 3
0: 15 18 2: . 15
o6 : Sequence
|
i7 : IX =ideal ring M0
3 2 2 3 2
o7 = ideal(- 3602x + 2676x x + 4148x x - 3153x - 29x x + 1064x x x +
0 0 1 0 1 1 0 2 0 1 2
------------------------------------------------------------------------
2 2 2 3 2 2
2979x x + 3231x x + 4343x x - 4844x - 569x x + 961x x x + 3038x x
1 2 0 2 1 2 2 0 3 0 1 3 1 3
------------------------------------------------------------------------
2 2 2 2
+ 1915x x x - 560x x x - 2674x x - 3634x x + 1166x x - 2749x x +
0 2 3 1 2 3 2 3 0 3 1 3 2 3
------------------------------------------------------------------------
2 2 2
790x x - 1943x x x - 2813x x + 1137x x x + 3432x x x + 3213x x -
0 4 0 1 4 1 4 0 2 4 1 2 4 2 4
------------------------------------------------------------------------
2 2 2
4817x x x + 4740x x x - 2868x x x + 2256x x + 3487x x - 2618x x )
0 3 4 1 3 4 2 3 4 0 4 1 4 2 4
o7 : Ideal of S
|
i8 : S===ring IX o8 = true |