All modules should be free modules over the same base ring, and the rank of the target of
f should be the product of the ranks of
G and
H. Recall that
** refers to the tensor product of modules, and that
dual G is a free module with the same rank as
G.
No computation is required. The resulting matrix has the same entries as
f, but in a different layout.
If
f is homogeneous, and
target f == G ** H,including the grading, then the resulting matrix will be homogeneous.
i1 : R = QQ[x_1 .. x_12];
|
i2 : f = genericMatrix(R,6,2)
o2 = | x_1 x_7 |
| x_2 x_8 |
| x_3 x_9 |
| x_4 x_10 |
| x_5 x_11 |
| x_6 x_12 |
6 2
o2 : Matrix R <--- R
|
i3 : g = adjoint1(f,R^2,R^3)
o3 = | x_1 x_4 x_7 x_10 |
| x_2 x_5 x_8 x_11 |
| x_3 x_6 x_9 x_12 |
3 4
o3 : Matrix R <--- R
|
i4 : isHomogeneous g
o4 = true
|