We investigate the feasibility of using computer algebra for solving L(2) system approximation problems. The first-order optimality conditions yield a set of polynomial equations, which can, in principle, be served using Grobner basis methods. A general solution along these lines would be tremendously useful, although it does not appear to be feasible at present, except for rather low McMillan degrees. We demonstrate that it can be feasible for specific examples; in such cases global optima can be found reliably. We show that the use of a Schwarz-like canonical form simplifies the structure of the problem.