[GiNaC-list] Simple question about how to solve for a simple non-linear system of equations.

[Ulrich Loup]

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.