If $g_i : C_i \rightarrow D_{d+i}$, and $h_j : D_j \rightarrow E_{e+j}$, then the composition corresponds to $f_i := h_{d+i} * g_i : C_i \rightarrow E_{i+d+e}$. In particular, the degree of the composition $f$ is the sum of the degrees of $g$ and $h$.
i1 : R = ZZ/101[a..d] o1 = R o1 : PolynomialRing |
i2 : C = freeResolution coker vars R
1 4 6 4 1
o2 = R <-- R <-- R <-- R <-- R
0 1 2 3 4
o2 : Complex
|
i3 : 3 * dd^C
1 4
o3 = 0 : R <------------------- R : 1
| 3a 3b 3c 3d |
4 6
1 : R <----------------------------------- R : 2
{1} | -3b -3c 0 -3d 0 0 |
{1} | 3a 0 -3c 0 -3d 0 |
{1} | 0 3a 3b 0 0 -3d |
{1} | 0 0 0 3a 3b 3c |
6 4
2 : R <--------------------------- R : 3
{2} | 3c 3d 0 0 |
{2} | -3b 0 3d 0 |
{2} | 3a 0 0 3d |
{2} | 0 -3b -3c 0 |
{2} | 0 3a 0 -3c |
{2} | 0 0 3a 3b |
4 1
3 : R <--------------- R : 4
{3} | -3d |
{3} | 3c |
{3} | -3b |
{3} | 3a |
o3 : ComplexMap
|
i4 : 0 * dd^C o4 = 0 o4 : ComplexMap |
i5 : dd^C * dd^C o5 = 0 o5 : ComplexMap |