I have a large (~1000 equations) overdetermined system of degree 3 polynomials with ~140 variables.
I would like to find a complete solution set for this system, however, the Gröbner basis seems to be too large to compute.
The first 100 equations can easily be factored/solved resulting in ~100 solutions.
Plugging one of these solutions into the remaining equations results in a new set of equations which also has a subset that can easily be solved.
Is there a way to obtain all solutions other than a brute force method of examining every possible case (the number of cases to consider grows quite fast)?