i1 : c = 2
o1 = 2
|
i2 : S = ZZ/32003[x_0..x_(c-1),a_(0,0)..a_(c-1,c-1)];
|
i3 : A = genericMatrix(S,a_(0,0),c,c);
2 2
o3 : Matrix S <-- S
|
i4 : f = matrix{{x_0..x_(c-1)}}*map(S^{c:-1},S^{c:-2},A)
o4 = | x_0a_(0,0)+x_1a_(0,1) x_0a_(1,0)+x_1a_(1,1) |
1 2
o4 : Matrix S <-- S
|
i5 : R = S/ideal f;
|
i6 : kR = R^1/ideal(x_0..x_(c-1))
o6 = cokernel | x_0 x_1 |
1
o6 : R-module, quotient of R
|
i7 : MF = matrixFactorization(f,highSyzygy kR)
o7 = {{2} | a_(0,0) -a_(0,1) a_(1,0) -a_(1,1) |, {3} | x_0 a_(0,1) 0
{2} | x_1 x_0 0 0 | {3} | -x_1 a_(0,0) 0
{2} | 0 0 x_1 x_0 | {3} | 0 0 x_0
{3} | 0 0 -x_1
------------------------------------------------------------------------
a_(1,1) 0 |, {2} | 0 0 1 |}
a_(1,0) 0 | {2} | 0 1 0 |
a_(0,1) a_(1,1) | {2} | 1 0 0 |
a_(0,0) a_(1,0) |
o7 : List
|
i8 : netList BRanks MF
+-+-+
o8 = |2|2|
+-+-+
|1|2|
+-+-+
|
i9 : netList dMaps MF
+-----------------------------------------+
o9 = |{2} | a_(0,0) -a_(0,1) | |
|{2} | x_1 x_0 | |
+-----------------------------------------+
|{2} | a_(0,0) -a_(0,1) a_(1,0) -a_(1,1) ||
|{2} | x_1 x_0 0 0 ||
|{2} | 0 0 x_1 x_0 ||
+-----------------------------------------+
|
i10 : netList bMaps MF
+------------------------+
o10 = |{2} | a_(0,0) -a_(0,1) ||
|{2} | x_1 x_0 ||
+------------------------+
|{2} | x_1 x_0 | |
+------------------------+
|
i11 : netList psiMaps MF
+------------------------+
o11 = |{2} | a_(1,0) -a_(1,1) ||
|{2} | 0 0 ||
+------------------------+
|