This is a very general/open-ended question.
I wonder if numerical solutions to large scale system of polynomial equations (in many variables) are used in physics at all. I am looking for some good reference to research level (open) problems in physics that involves large scale polynomial systems that cannot be solved by software packages like Mathematica or Maple within any reasonable amount of time.
Ideally, these problems
- focus on the complex solutions (as oppose to integer or rational solutions)
- relatively easy to understand for outsiders (with sufficient math background)