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.

For example:

$\displaystyle

\left\{

\begin{array}{rr}

1+x_1-x_1 x_2 = 0\\

1+x_1-3 x_1 x_2+\frac{3}{2} x_1 x_2^2-\frac{1}{6}x_1 x_2^3 = 0

\end{array}

$

(Of course, my system is biger than that very much). I only need one of its solution, which satisfied condition $\displaystyle x_i > 0$. 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