I am wondering whether there is any software package that can compute Groebner bases for noncommutative algebras defined over the field of rational functions $\mathbb{Q}(q)$. 


I have tried the GAP package [GBNP](http://www.gap-system.org/Packages/gbnp.html) but I can't seem to even construct $\mathbb{Q}(q)$ in it, much less define an algebra over it.


I have also tried the Mathematica package [NCGB](http://math.ucsd.edu/~ncalg/) released by UC San Diego, but it suggests that I specialize to a rational value of $q$, which is not what I want to do.


Free software is preferred, but I am also interested in finding out if there is proprietary software that can do the job. Does Magma do this?



Software for noncommutative Groebner bases over rational function fields
I think Magma is fairly general in base rings. Following their example:



```
> Q<q> := FunctionField(Rationals());
> F<x,y,z> := FreeAlgebra(Q,3);
> B := [x^2-q*y*z,q^2*x*y-y*z,y*x*q-z^2,q*y^3-x*z];
> I := ideal<F | B>;
> GroebnerBasis(I);

```

I am not sure exactly what functionality you want, but if it can handle the basis operations, then Groebner should be possible (though may be slow).


