An "external" R-degree is a list of integers of length equal to (degreeLength R) - (degreeLength k). See Encoding diagrams as modules for more discussion about internal and external degrees for a ring.
A graded R-module has a component $R_x$ in every external degree $x$, and this component is a $k$-module. If $r \in R$ has degree $y-x$, then multiplication by $r$ gives a $k$-linear map $R_x \to R_y$. This is the map that is returned by structureMap.
Only one of $x$ and $y$ needs to be supplied if $r$ is nonzero, since then the other degree can be inferred.
i1 : k = QQ[s, t, u]; R = k[x, y]; m = matrix {{s*x^2+t*x*y+u*y^2}}; M = coker m
1 1
o3 : Matrix R <--- R
o4 = cokernel | sx2+txy+uy2 |
1
o4 : R-module, quotient of R
|
i5 : phi = structureMap({4}, {7}, x^2*y, M)
o5 = | 0 0 0 0 0 |
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 1 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 1 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
o5 : Matrix
|
i6 : source phi
o6 = cokernel | s 0 0 |
| t s 0 |
| u t s |
| 0 u t |
| 0 0 u |
5
o6 : k-module, quotient of k
|
i7 : target phi
o7 = cokernel | s 0 0 0 0 0 |
| t s 0 0 0 0 |
| u t s 0 0 0 |
| 0 u t s 0 0 |
| 0 0 u t s 0 |
| 0 0 0 u t s |
| 0 0 0 0 u t |
| 0 0 0 0 0 u |
8
o7 : k-module, quotient of k
|
The object structureMap is a method function.