Description
The output of
transpose is a map from the duals of the original source and target free modules. See the degree of the target module in the following example
i1 : S = ZZ/10007[x,y,z];
|
i2 : F = res ideal vars S;
|
i3 : F.dd
1 3
o3 = 0 : S <------------- S : 1
| x y z |
3 3
1 : S <-------------------- S : 2
{1} | -y -z 0 |
{1} | x 0 -z |
{1} | 0 x y |
3 1
2 : S <-------------- S : 3
{2} | z |
{2} | -y |
{2} | x |
1
3 : S <----- 0 : 4
0
o3 : ChainComplexMap
|
i4 : transpose F.dd
1
o4 = -4 : 0 <----- S : -3
0
1 3
-3 : S <------------------- S : -2
{-3} | z -y x |
3 3
-2 : S <-------------------- S : -1
{-2} | y -x 0 |
{-2} | z 0 -x |
{-2} | 0 z -y |
3 1
-1 : S <-------------- S : 0
{-1} | x |
{-1} | y |
{-1} | z |
o4 : ChainComplexMap
|
Note that
M2 treats the differentials of a chain complex map as map of degree -1.