i1 : pieri({3,1}, {1}, QQ^3) -- removes the first box from the partition {3,1}
o1 = | 3x_0 0 x_1 0 x_2 0 0 0 0 0 0 0 0
| 0 3x_0 0 x_1 0 x_2 0 0 0 0 0 0 0
| 0 0 2x_0 0 0 0 2x_1 0 x_2 0 0 0 0
| 0 0 0 2x_0 0 0 0 2x_1 0 x_2 0 0 0
| 0 0 0 0 2x_0 0 0 0 x_1 0 2x_2 0 0
| 0 0 0 0 0 2x_0 0 0 0 x_1 0 2x_2 0
| 0 0 0 0 0 0 0 x_0 -1/2x_0 0 0 0 3x_1
| 0 0 0 0 0 0 0 0 0 x_0 -2x_0 0 0
------------------------------------------------------------------------
0 0 |
0 0 |
0 0 |
0 0 |
0 0 |
0 0 |
x_2 0 |
2x_1 2x_2 |
8 15
o1 : Matrix (QQ[x , x , x ]) <--- (QQ[x , x , x ])
0 1 2 0 1 2
|
i2 : res coker oo -- resolve this map
8 15 10 3
o2 = (QQ[x , x , x ]) <-- (QQ[x , x , x ]) <-- (QQ[x , x , x ]) <-- (QQ[x , x , x ]) <-- 0
0 1 2 0 1 2 0 1 2 0 1 2
4
0 1 2 3
o2 : ChainComplex
|