On Nov 30, 1:01 am, Daniel Lichtblau <d...@wolfram.com> wrote: > Version 8 Solve attempts to compute a lexicographic Groebner basis over > a field of fractions in the parameters. I gather this turns out to be > very difficult for this example, and it hangs here. I do not know > offhand whether this indicates a limitation of our Groebnerbasis code, > or this is just an intrinsically difficult computation.
Unless evaluation and interpolation are used extensively, computing over the field of fractions is intrinsically harder. The gain is that you remove content from all the polynomials in each step, which may help simplify the system. In practice you can just preprocess the generators because once the Groebner algorithms start running this is quite rare. A fast modular method over Q using a block order, with parameters below the original variables, is often better for a small number of parameters.