Construction of a subalgebra of the Weyl-Algebra

Hi everyone,

i'm currently writing my master thesis and got stuck at a problem which i want to implement.
In my thesis I want to work over a subset (K-subalgebra) of the Weyl-Algebra, which is generated by (x, x*dx), and want to perform Gröbner basis -, syzygie module -, normal form computations ect..
Is there any way to construkt such a set V ( which should be something like V=QQ[x,x*dx]/(dx*x-x*dx=1) ) and tell Singular to perform the already implemented algorithms over V?

Thanks a lot
Jannis

sagbi.lib works with subalgebras. (see https://www.singular.uni-kl.de/Manual/4-1-3/sing_1439.htm),
It was not thought for working over non-commative rings,
but some of these techniques may applay alsoin your case of the Weyl algabera.