Sheldon,
> I am interested in computing the intersections of the curves
>
> $C_1(t,n), C_2(t,n)$ in the unit square for $n=12$.
Fabrizio Caruso, whose name I mentioned before in connection
with the zeilberger package, also wrote the package sarag
("some algorithms in real algebraic geometry"). I believe
it is relevant here. The documentation for it is in the file
maxima/share/contrib/sarag/readme.txt (sorry, it is not yet
integrated into the help system; I was working on that but
didn't finish it.) I don't really know how to use sarag; I think
you might have to ask Fabrizio about it.
Hope this helps
Robert