Hello. I have a research project and need to solve the system of nonlinear polynomial equations like that:
1.The polynomial equations have degrees 2, 4, 6, 8 respectively...........
2.The system is positive-dimensional.
(Of course, my system is biger than that very much). I only need one of its solution, which satisfied condition . The system is very unstable, it can not be solved by any numerical method, such as Newton method, Homotopy method or so... and needs a "arbitrary precision arithmetic" environment to calculate.
I use Maple, command Triangularize - package RegularChains - to transform this system to triangular form. That command gave me nice solution, but it only works for system up to 4 equations. For system consists of 6 equations, Maple used ~2Gigabytes of RAM and gave up.
So, do you know how to solve this problem? Which method is efficient to my system? Thank you very much for your help