Alan Adler's long letter to the GAP-forum of August 24 was
unfortunately rejected by the mail server because the sender's address
was not that of a member of the GAP-forum. It was then sent to the
forum by Frank Celler. In order to avoid such delays please make sure
that you write to the GAP-forum from the address with which you
originally registered with the forum. When you change your address,
please 'unsubscribe' and subscribe again with your new address.

As to Alan Adler's letter: Yes, GAP does not provide all that a CA
system like Reduce or Maple has. (For that reason we do ourselves use
in particular Maple in our work and - to comment on Gregor Kemper's
last remark - Maple or Reduce or some of the others are no no-no-words
in the GAP-forum at all!) In particular while GAP got a (hopefully
reasonable) polynomial arithmetic for univariate polynomials with
version 3.2 it does not have (yet?!) an efficient multivariate
polynomial arithmetic. (Since polynomials can be formed over arbitrary
coefficient rings you can mimic a polynomial in two variables by a
polynomial over the ring of univariate polynomials and so on, but that
is not suitable for serious efficient computation).

However in answer to some of the problems, Alan Adler addresses: There
are systems for handling multivariate puolynomials very efficiently
that are free of charge (although maybe formally not public domain in
the same way that GAP is not public domain, namely in that a copyright
is formulated that forbids commercialisation by third parties). I
particularly mention MACAULAY and CoCoA.

By the way, if you want rather comprehensive information on presently
available CA systems (including CGT), you may want to consult the
report "Computeralgebra in Deutschland" published by "Fachgruppe
Computeralgebra of GI, DMV, and GAMM" which in spite of its
understating title gives a fairly broad description on the present
worldwide state of activities in algebraic and symbolic computation as
well as good characterisations of 39 systems and packages for such
computations together with information where and under which
conditions to obtain them.

Joachim Neubueser