Description
Recall that ** refers to the tensor product of modules.
i1 : R = QQ[x_1 .. x_24];
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i2 : f = genericMatrix(R,2,4*3)
o2 = | x_1 x_3 x_5 x_7 x_9 x_11 x_13 x_15 x_17 x_19 x_21 x_23 |
| x_2 x_4 x_6 x_8 x_10 x_12 x_14 x_16 x_18 x_20 x_22 x_24 |
2 12
o2 : Matrix R <--- R
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i3 : isHomogeneous f
o3 = true
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i4 : g = adjoint(f,R^4,R^3)
o4 = | x_1 x_7 x_13 x_19 |
| x_2 x_8 x_14 x_20 |
| x_3 x_9 x_15 x_21 |
| x_4 x_10 x_16 x_22 |
| x_5 x_11 x_17 x_23 |
| x_6 x_12 x_18 x_24 |
6 4
o4 : Matrix R <--- R
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If f is homogeneous, and source f === F ** G (including the grading), then the resulting matrix will be homogeneous.
i5 : g = adjoint(f,R^4,R^{-1,-1,-1})
o5 = {-1} | x_1 x_7 x_13 x_19 |
{-1} | x_2 x_8 x_14 x_20 |
{-1} | x_3 x_9 x_15 x_21 |
{-1} | x_4 x_10 x_16 x_22 |
{-1} | x_5 x_11 x_17 x_23 |
{-1} | x_6 x_12 x_18 x_24 |
6 4
o5 : Matrix R <--- R
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i6 : isHomogeneous g
o6 = true
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