I have a system of polynomial equations with the unknowns being real numbers. The set of solutions is infinite. What software can I use to compute the real dimension of the solution set?
The CAD-based approach, which is implemented in various computer algebra systems, is too slow for my problems. I found several recent papers on other algorithms for finding the dimension but they were not accompanied with an open-source implementation.
I am looking for the implementation of some (preferably) non-randomized and exact method for computing the exact value of the dimension.