Hi Hedos!
> I'm interested about how one can build a simple symbolic mathematic systems
> on a computer.
Why don't you contribute to an existing CAS instead? That way you can
learn the same or even more and you work actually has some value ...
Is this some kind of home work example?
> I thought I would ask on here, hopefully some of you can
> point me to ressources or help me find out where to start. I'd just like to
> learn how to build something basic, such as polynomial manipulation, to
> begin.
I think the best pointer I can give you is the following article:
Note that it explicitely talks about polynomial manipulation ...
http://lists.nongnu.org/archive/html/axiom-developer/2007-03/msg00211.html
HTH,
Harald