Hello,
Z> how to solve a nonlinear system of equations.
There is no general method to solve non-linear equations. Even for a single algebraic equation of degree >4 there is no a closed formula (see, Galois theory). So, either you need program a particular method (if known for your problem) yourself, or use numerical approximations.
Although there is no general closed formula to solve non-linear equations, there are some exact methods to solve a system of non-linear polynomial equations (and even inequalities), e.g., the cylindrical algebraic decomposition (CAD) method. However, in order to implement this method via ginac, a lot of things have to be set up. In particular, it is important to have a data structure representing a real root of a polynomial, because such a root does not necessarily need to be a rational number or a radical expression as, e.g., sqrt(2) (cf. the real root of x^5-2x^4+3x^3-5x^2+x-1). If you are interested in such exact methods, you can find a preliminary, ginac-based implementation of the CAD method on http://ginacra.sourceforge.net/. We are still working on the next release, so just send an email for an up-to-date version. Many regards, Ulrich.