Description
The chain complex
M should be a direct sum, and the result is the map obtained by projection onto the sum of the components numbered or named
i, j, ..., k. Free modules are regarded as direct sums of modules.
i1 : M = ZZ^2 ++ ZZ^3
5
o1 = ZZ
o1 : ZZ-module, free
|
i2 : M^[0]
o2 = | 1 0 0 0 0 |
| 0 1 0 0 0 |
2 5
o2 : Matrix ZZ <-- ZZ
|
i3 : M^[1]
o3 = | 0 0 1 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 1 |
3 5
o3 : Matrix ZZ <-- ZZ
|
i4 : M^[1,0]
o4 = | 0 0 1 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 1 |
| 1 0 0 0 0 |
| 0 1 0 0 0 |
5 5
o4 : Matrix ZZ <-- ZZ
|
If the components have been given names (see
directSum), use those instead.
i5 : R = QQ[x,y,z];
|
i6 : C = res coker vars R
1 3 3 1
o6 = R <-- R <-- R <-- R <-- 0
0 1 2 3 4
o6 : ChainComplex
|
i7 : D = (a=>C) ++ (b=>C)
2 6 6 2
o7 = R <-- R <-- R <-- R <-- 0
0 1 2 3 4
o7 : ChainComplex
|
i8 : D^[a]
1 2
o8 = 0 : R <----------- R : 0
| 1 0 |
3 6
1 : R <----------------------- R : 1
{1} | 1 0 0 0 0 0 |
{1} | 0 1 0 0 0 0 |
{1} | 0 0 1 0 0 0 |
3 6
2 : R <----------------------- R : 2
{2} | 1 0 0 0 0 0 |
{2} | 0 1 0 0 0 0 |
{2} | 0 0 1 0 0 0 |
1 2
3 : R <--------------- R : 3
{3} | 1 0 |
4 : 0 <----- 0 : 4
0
o8 : ChainComplexMap
|