i1 : F = mooreMF(0)
3 3 3
o1 = (QQ[a ..a , x ..x ]) <-- (QQ[a ..a , x ..x ]) <-- (QQ[a ..a , x ..x ])
0 2 0 2 0 2 0 2 0 2 0 2
0 1 0
o1 : ZZdFactorization
|
i2 : F.dd
3 3
o2 = 1 : (QQ[a ..a , x ..x ]) <-------------------------------------------------------------------------------------- (QQ[a ..a , x ..x ]) : 0
0 2 0 2 {2} | a_1a_2x_0^2-a_0^2x_1x_2 a_0a_2x_1^2-a_1^2x_0x_2 -a_2^2x_0x_1+a_0a_1x_2^2 | 0 2 0 2
{2} | -a_1^2x_0x_1+a_0a_2x_2^2 a_0a_1x_0^2-a_2^2x_1x_2 a_1a_2x_1^2-a_0^2x_0x_2 |
{2} | a_0a_1x_1^2-a_2^2x_0x_2 -a_0^2x_0x_1+a_1a_2x_2^2 a_0a_2x_0^2-a_1^2x_1x_2 |
3 3
0 : (QQ[a ..a , x ..x ]) <-------------------------------- (QQ[a ..a , x ..x ]) : 1
0 2 0 2 {4} | a_0x_0 a_1x_2 a_2x_1 | 0 2 0 2
{4} | a_1x_1 a_2x_0 a_0x_2 |
{4} | a_2x_2 a_0x_1 a_1x_0 |
o2 : ZZdFactorizationMap
|
i3 : potential F
3 3 3 3 3 3
o3 = a a a x + a a a x - a x x x - a x x x - a x x x + a a a x
0 1 2 0 0 1 2 1 0 0 1 2 1 0 1 2 2 0 1 2 0 1 2 2
o3 : QQ[a ..a , x ..x ]
0 2 0 2
|
i4 : E = Hom(F,F)
18 18 18
o4 = (QQ[a ..a , x ..x ]) <-- (QQ[a ..a , x ..x ]) <-- (QQ[a ..a , x ..x ])
0 2 0 2 0 2 0 2 0 2 0 2
0 1 0
o4 : ZZdFactorization
|
i5 : prune HH_1 E
o5 = cokernel | a_1 a_0 0 0 0 0 -a_2 0 0 0 0 -a_2 0 0 0 0 |
| 0 0 x_2 x_0 0 0 0 x_1 0 0 0 0 0 0 0 0 |
| 0 0 0 0 a_2 a_1 a_0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 x_2 x_1 x_0 0 0 0 0 0 -x_2 |
| 0 0 0 0 0 0 0 0 0 0 a_2 a_1 a_0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 0 0 0 x_2 x_1 x_0 |
6
o5 : QQ[a ..a , x ..x ]-module, quotient of (QQ[a ..a , x ..x ])
0 2 0 2 0 2 0 2
|
i6 : prune HH_0 E
o6 = cokernel | a_1a_2x_1^2-a_0^2x_0x_2 a_1^2x_0x_1-a_0a_2x_2^2 a_0a_1x_0^2-a_2^2x_1x_2 a_0a_2x_1^2-a_1^2x_0x_2 a_0^2x_0x_1-a_1a_2x_2^2 -a_2^2x_0x_1+a_0a_1x_2^2 -a_0a_2x_0^2+a_1^2x_1x_2 -a_1a_2x_0^2+a_0^2x_1x_2 a_0a_1x_1^2-a_2^2x_0x_2 |
1
o6 : QQ[a ..a , x ..x ]-module, quotient of (QQ[a ..a , x ..x ])
0 2 0 2 0 2 0 2
|
i7 : netList (ann oo)_* --recover entries of 0th differential
+---------------+
| 2 2 |
o7 = |a a x - a x x |
| 1 2 1 0 0 2|
+---------------+
| 2 2 |
|a a x - a x x |
| 0 2 1 1 0 2|
+---------------+
| 2 2 |
|a a x - a x x |
| 0 1 1 2 0 2|
+---------------+
| 2 2|
|a x x - a a x |
| 2 0 1 0 1 2|
+---------------+
| 2 2|
|a x x - a a x |
| 1 0 1 0 2 2|
+---------------+
| 2 2|
|a x x - a a x |
| 0 0 1 1 2 2|
+---------------+
| 2 2 |
|a a x - a x x |
| 1 2 0 0 1 2|
+---------------+
| 2 2 |
|a a x - a x x |
| 0 2 0 1 1 2|
+---------------+
| 2 2 |
|a a x - a x x |
| 0 1 0 2 1 2|
+---------------+
|