My question here is very computational. My problem is in mathematical physics, so I want to ask the community what kind of software they use to do the following computation if there is any? Let $$L_{n}=-\frac{n+1}{s} (u+v)n\frac{\partial}{\partial n} +\sum_{j=1}^{\infty} p_j (n+j)\frac{\partial}{\partial p_{n+j}}+\sum_{i+j=n}ij\frac{\partial^2}{\partial p_i \partial p_j} $$
For $n,m\geq 0$ it satisfies following equation $$[L_m,L_n]=(m-n)L_{m+n} $$ where $[]$ denote the commutation bracket in Weyl algebra. Notice that there infinitely many $p_i$.