I want to work with determinants of matrices where some or all entries in the matrices are differential operators. Please see the attached file for an example.
What I am looking for is a way to
a) Make the operators (automatically) compose without manually having to insert @'s in the expression Mathematica outputs. This gets tiresome and error-prone with even 4x4 matrices. This should (preferably) be done before the operators act on the expression. Maybe using Composition in a clever way?
b) Make the differentiation work even if the operators carry negative sign. Now I have to manually add parentheses to perform the differentiation.
I understand that this is really an operator algebra I could (should?) define, but it seems I'm almost there as-is.
Any help much appreciated!
Attachment: comp-diff-op.nb, URL: ,