Usage
adjoint L
Parameter | Type | Description |
---|---|---|
L | A differential operator |
Returns
Returns the adjoint operator of , i.e.
where
and is the product in .
Example
It can happen that has a nontrivial rational kernel, while has a trivial one:
1 --> L := x*D^3 + D^2 - x^2*D - 2*x; 2 --> LL := adjoint(L); 3 --> tex(LL);
So , while has no nonzero rational solution:
4 --> K := kernel(L); 5 --> tex(K);
We also verify that :
6 --> tex(L - adjoint(LL));