The encoding of a long exact sequence as a module is described in detail in longExactSequence
i1 : R = QQ[d]/d^2; |
i2 : M = coker map(R^{-1,-1,-1,-1,-1,0,0,0,0},R^{-1,-1,-1,-2,-2,-2,-2,-2},
{{0,0,0,d,0,0,0,0},{0,0,0,0,d,0,0,0},{0,0,0,0,0,d,0,0},
{0,0,0,0,0,0,d,0},{0,0,0,0,0,0,0,d},{-4*d,4*d,4*d,0,0,0,0,0},
{5*d,0,0,0,0,0,0,0},{0,5*d,0,0,0,0,0,0},{0,0,5*d,0,0,0,0,0}});
|
i3 : N = coker map(R^{-1,-1,0,0,0,1,1},R^{0,-1,-1,-2,-2},
{{0,0,0,d,0},{0,0,0,0,d},{0,0,-4*d,0,0},{0,d,0,0,0},
{0,0,3*d,0,0},{0,0,0,0,0},{d,0,0,0,0}});
|
i4 : f = map(N, M, {{1,1,1,1,1,0,0,0,0},{1,1,1,1,1,0,0,0,0},{d,d,d,d,d,-14,-12,4,4},
{0,0,0,0,0,1,1,1,1},{0,0,0,0,0,3,3,3,3},{0,0,0,0,0,d,d,d,0},
{0,0,0,0,0,0,0,0,0}});
o4 : Matrix
|
i5 : LES = longExactSequence f;
warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
|
i6 : expectExactCouple LES; |
i7 : excerptLES(0,2,LES)
o7 = .- -> 0
0 (
\
2 1 0 \
.- -> QQ - - - - -> QQ - - -> 0 - -'
| 0 0 0 0 1 |( | 0 1 |
| 0 0 0 0 0 | \
| 0 1 0 0 0 |
| 0 0 1 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 1 |
2 5 | 0 0 0 0 0 | 5 \
.- -> QQ - - - - -> QQ - - - - - - - -> QQ - -'
| 0 0 1 | ( | 0 1 |
| 0 0 0 | \ | 0 0 |
| 0 0 |
| 0 0 |
| 0 0 |
| 0 1 0 |
| 0 0 1 |
1 3 | 0 0 0 | 3 \
.- -> QQ - - - -> QQ - - - - - -> QQ - -'
0 ( | 1 |
\ | 0 |
| 0 |
\
0 - -'
|
The object excerptLES is a method function.