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This is a repost of my question at MSE from 7 months ago, to which I haven't been able to find an answer yet. I am looking for a CAS (possibly incl. additional packages/libraries) that can compute ...

This is a noncommutative version of these three previous questions: differential operator power coefficients Сlosed formula for $(g\partial)^n$ A Leibniz-like formula for $(f(x) \frac{d}{dx})^n f(x)$? ...

Let $K=\mathbb{C}((t))$ and let $K_m=\mathbb{C}((t^{1/m}))$. let $K\{x\}$ denote the ring of twisted polynomials. The addition in this ring is defined as usual, but the multiplication is adjusted by ...

Let F be a field. Recall that an additive map $d: F\rightarrow F$ is said to be a derivation if $d(ab)=ad(b)+d(a)b$. Now let $F$ be a ring and let $d$ be a derivation of $F$. Examples I have in mind ...