Hi!
I have presented my new library
on real algebraic geometry at
Mega 2005 in Alghero, Italy
(conference on computational algebraic geometry).
The library is also used in the new
edition of "Algorithms in Real Algebraic
Geometry" by Basu, Pollack, Roy.
The new edition will be a free "active book"
that will be available for download.
The book is written in TexMacs and
the "active" part in Maxima.
I will send you soon the library.
It would be nice if some of you would
let me know about any bug.
So far the library does:
(1) faster (seems to me)
gaussian elimination and triangularization
then in built-in maxima functions
(2) signed remainder sequence and signed subresultant sequence
(3) real root counting through Cauchy Index
and Tarski query
(4) real root isolation (with sign of other polynomials)
(5) efficient sign determination
(i.e. possible signs of polynomials at
roots of other polynomials)
(6) thom encoding and real roots in
general real closed fields (not necessarily
archimedean).
The library will do other things like:
(1) faster gcd
(2) topology of curves
Once the library is finished and reaches
a stable status, I would like to have it
as part of Maxima.
Regards
Fabrizio