Sorry. That was $k^{46}$.

I was able to get both of those equations as polynomials with rational coefficients. Eqn1 has bout 35 terms in it, with highest powers of $r^4$, $k^8$, and $f^4$. However, the polynomial version of Eqn2 has about 450 terms and fills up three screens with them, with powers of $r^8$ and $k^46$. Needless to say when I try and then find the Groebner bases for these polynomials, the symbolic math toolbox in matlab chokes on it. I left it running for a few hours with no avail.

Thanks for answering. I've never heard of Groebner bases before (I'm an engineer as opposed to a mathematician), but I did some googling and I think I may understand the basic concept. I'll do some reading and get back to you.