An "external" degree deg is one so that, given a degree deg' for the coefficient ring of R, the concatenation (deg | deg') is a valid degree for R. So an external degree is a list of integers of length (degreeLength R) - (degreeLength coefficientRing R).
See Encoding diagrams as modules for more discussion about internal and external degrees for a ring.
If you want to evaluate at an internal degree, you will need to restack the module so that the degree becomes external. See restackModule and restackRing for information about how to do this.
i1 : S = QQ[s, t, u]; R = S[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 : N = evaluateInDegree({4}, M)
o5 = cokernel | s 0 0 |
| t s 0 |
| u t s |
| 0 u t |
| 0 0 u |
5
o5 : S-module, quotient of S
|
i6 : apply(10, i -> hilbertFunction({i}, N))
o6 = {5, 12, 21, 32, 45, 60, 77, 96, 117, 140}
o6 : List
|
i7 : (F, f) = flattenRing R; apply(10, i -> hilbertFunction({4, i}, f ** M))
o8 = {5, 12, 21, 32, 45, 60, 77, 96, 117, 140}
o8 : List
|
The object evaluateInDegree is a method function.