use lazy q-commuting formal power series ?

[fchapoton]

One could maybe make good use of

sage: B = matrix([[0,1,2],[-1,0,3],[-2,-3,0]])
sage: q = ZZ['q'].gen()
sage: R.<x,y,z> = algebras.qCommutingPolynomials(q, B)
sage: R.formal_series_ring()
Lazy completion of q-commuting polynomial ring in x, y, z over Univariate Polynomial Ring in q over Integer Ring with matrix:
[ 0  1  2]
[-1  0  3]
[-2 -3  0]

?

[smzg]

This structure is indeed very similar to the quantum torus implemented in TMPolynomialRing, but most of the methods will have to be rewritten, so I am not sure about any advantage of using it.

[fchapoton]

There may be an advantage in terms of speed and code concision. There is also an interest in leaving to sagemath developers the burden to maintain the code in a working state. This also applies for instance to your poset code, that may be integrated inside sage without too much effort.