As most of you know Maxima
has an implementation of Groebner bases
which uses some of the smart criteria
(sugar, product criterion, etc...)
that have been devised to speed up
the computation.
Nevetheless the state of the art in "fast"
Groebner bases are nowadays F4 and F5 (by Faugere),
which are new variations of the old Macaulay
algorithm.
Macaulay-like algorithms boil down to linear
algebra on huge matrices, which under
some assumptions are minimal (semi-regularity),
whereas Buchberger's algorithm selects the reductions
by various criteria, which are not always optimal.
It would be nice to have at least F4 in Maxima.
As far as I know F4 is implemented in the
Magma computer algebra system.
At the moment I am working on something
similar to F4 over Z_2.
Once I am done I'll release it in a package
but a more general F4 would be preferable.
Fabrizio