[GiNaC-list] Simple question about how to solve for a simple non-linear system of equations.
Ulrich Loup
loup at cs.rwth-aachen.de
Sat Jan 5 01:56:27 CET 2013
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.
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