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I am curious to see what does Sage answers on this particular example. If there is no asumption on the di, the following non equivalent answers are possible:

[   d0     1     0    0]
[    0    d0     1    0]
[    0     0    d0    1]
[    0     0     0   d0]

[   d0     0     0    0]
[    0    d0     0    0]
[    0     0    d0    0]
[    0     0     0   d0]