### Solve a "big" polynomial system numerically

I would like to solve numerically a polynomial system with around 10^5 variables and 10^7 equations. Each equation is of degree 4 with integer coefficients and contains around 10 variables, so that the **jacobian** of the system is a very "**hollow**" matrix with **integer entries**.

Let X=[x_0,x_1, x_2,...] and E=[eq_0,eq_1, eq_2...] the list of variables and equations :

Is there a SAGE function f(E,X) which
find numerically solutions for such a system?

Is SAGE relevant for such intensive
computation ?

I think the code needs to be **100% cython**, for not losing time.

My computer has a hard disk of 980 Go, 4Go of RAM and its processor "Intel Core i5 CPU 760 @ 2.80GHz × 4" is around 10^9 FLOPS.

I guess my computer is not enough powerful for doing such computation in a reasonable time :

The jacobian J is a (10^5)x(10^7) matrix, so for example, the Gauss-Newton algorithm would require around 1000 Go of RAM and 10^16 operations.

I know very few things in numerical
analysis, so some advices would be
welcome.