Every module in Macaulay2 has, at least implicitly, a generator matrix and a matrix of relations, both of which are matrices between free modules. This function returns the generator matrix. The module is generated by (the images of) the columns of this matrix.
i1 : R = GF(8,Variable=>a)
GC Warning: Repeated allocation of very large block (appr. size 1167360):
May lead to memory leak and poor performance.
o1 = R
o1 : GaloisField
|
i2 : f = R_0 ++ R_0^2 ++ R_0^3 ++ R_0^4
o2 = | a 0 0 0 |
| 0 a2 0 0 |
| 0 0 a+1 0 |
| 0 0 0 a2+a |
4 4
o2 : Matrix R <--- R
|
i3 : generators image f
o3 = | a 0 0 0 |
| 0 a2 0 0 |
| 0 0 a+1 0 |
| 0 0 0 a2+a |
4 4
o3 : Matrix R <--- R
|
i4 : generators cokernel f
o4 = | 1 0 0 0 |
| 0 1 0 0 |
| 0 0 1 0 |
| 0 0 0 1 |
4 4
o4 : Matrix R <--- R
|