It seems someone wants to implement CAD in Maxima.
I would suggest using the SARAG package as
a starting point.
It has been developed primarily by me but a few
other people from the Univ. of Rennes I have
contributed new features and improments.
The Maxima package "SARAG" is a real algebraic geometry package.
Among the things you find in SARAG:
subresultant, Bernstein polynomials,
Cauchy index, isolation of real roots,
sign determination, Thom encodings,
topology of curves (with nice plots),
certificate of positivity for both
univariate and multivariate polynomials (with nice plots).
The SARAG source is included in Maxima together with a small manual
that can be found in the source directory.
For any help please do not esitate to contact me.
Fabrizio