I am having trouble solving a real polynomial
system. It has about 100-200 variables and 200-400 equations and 2-7 symbolic parameters, and I am interested in a single solution.
Functions I have tried:
Solve[...] / Reduce[..., Reals]:
These take extremely long even if I make the system a lot smaller (60 variables and 100 equations). As I need to use my university computer during the day, I do not know if the computation would be complete when left alone for more than a weekend.
Does not work because I need a few symbolic model parameters. The equations are linear in the model parameters and the results should depend linearly on them. (Setting all parameters and variables to zero makes all equations true.)
I know many cases in which simple solutions exist, with only two or three variables being non-zero. Even in these simple cases, I cannot reproduce the result with Mathematica's Solve or Reduce functions (I cancelled the calculation after a day without a result), so I think the problem may be that Mathematica is trying to find all solutions. If I overconstrain the system so that the simple solutions are the only ones left, Mathematica can find them quickly with its Solve function.
Is there a way to find a single solution to a polynomial system faster than by just solving the whole system, or is there a way to make Solve compute faster?