# Multivariate Polynomials over Rational Function Fields

Is it possible to define multivariate polynomials where the coefficients lie in a rational function field and do Groebner basis computations on them? Maple, Reduce and Axiom support this. For example I would like to be able to compute the Groebner basis of the polynomials

```
{v * x^2 + y, u* x * y + y^2}
```

where the polynomials belong to the ring Q(u,v)[x,y].

I tried the following

```
B.<u,v> = PolynomialRing(QQ, 'u', 'v')
R.<x,y> = PolynomialRing(B, 'x', 'y')
I = R.ideal(v * x^2 + y, u* x * y + y^2)
g = I.groebner_basis()
```

This fails with the error

```
TypeError: Can only reduce polynomials over fields.
```