Finding Grobner Bases in Coefficient Rings Other than Q

We would like to determine the Grobner basis of an ideal F in the coefficient ring Q[sqrt(5), sqrt(3), sqrt(2)]. However, Maple always assumes the ring of coefficients to be Q:

> F:=[x^2-sqrt(5)*x*y+3*x*z+2*sqrt(5)*z^2, x*y-sqrt(2)*z^2, 2*x*y+sqrt(3)*z^2];                     

           2    1/2                 1/2  2           1/2  2             1/2  2
    F := [x  - 5   x y + 3 x z + 2 5    z ,   x y - 2    z ,   2 x y + 3    z ]

> X:=[x,y,z]:                                          
> G:=gbasis(F,X,plex);                                 
Error, (in grobner/iplex/reduce) cannot evaluate boolean

Here is how to get around this problem:

In ideal F substitute variables for the square roots, for example let a = sqrt(5), let b = sqrt(3), and let c = sqrt(2).
Find the minimal polynomial over Q for each of the square roots, and include these new polynomials in F. Each minimal polynomial should be in the variable used for the substitution.
Make the term orders of the "new" variables lower than those of the original variables.
Compute the Grobner basis for F as an ideal in Q[x,y,z,a,b,c], (that is, in coefficient ring Q).

> F:=[x^2-a*x*y+3*x*z+2*a*z^2, x*y-c*z^2, 2*x*y+b*z^2, a^2-5, b^2-3, c^2-2];

     2                  2            2              2    2        2        2
F:=[x  - axy + 3xz + 2az ,  x y - c z ,  2 x y + b z ,  a  - 5,  b  - 3,  c  - 2]

> X:=[x,y,z,a,b,c]:
> G:=gbasis(F,X,plex);

               2                    2     2         2         2
        G := [x  + 3 x z,   x y,   z ,   a  - 5,   b  - 3,   c  - 2]

Finally, by evaluating the ideal G at a = sqrt(5), b = sqrt(3), and c = sqrt(2) get a new ideal,
[x² + 3 x z, x y, z²]
which is the ideal we seek in our particular coefficient ring.