[Axiom-mail] Re: aldor

[Bertfried Fauser]

Dear Tim!

        thank you for the offer to ask questions. But let me beforehand
explain what my background is.

        By the way you should drop 'Professor', which is untrue (hopefully
not for ever). I am working in quantum field theory and need urgently
abstract algebra, however I am not canonically trained in this field. The
last three years showed me that I need urgently things like categories,
functors, but also Groebner bases for non-commutative algebras (that's not
yet solved on my side).
        My interest in computer algebra started when I used the Clifford
package of Rafal Ablamowicz (TN Tech Univ. Cookevile) for my work in 1996.
First I asked for procedures, then I was beta tester, then I wrote an own
package on Clifford Hopf algebras and since last September I am coauthor
of the Clifford/Bigebra package. This was done in maple, since Rafal had
by chance a maple around when he started his first hack.
        The package is awkward, since it grew up from a quick and dirty
hack and we had to do much nasty tricks to speed it up and make it usable
for a general purpose. However, you might acknowledge that this was also
due my very basic programming skills.

        For me, research has priority and I would not spend at the current
time to much efforts in using CAS systems in teaching, since in a physics
department (I am member of an astrophysics group, hahaha ..) I cannot say
the word category loudly (even if some guests which I invited did so).
Things are different with Rafal, he uses the software for teaching
mathematics and engineering students. Some of our algorithms are very fast
an my be useful in projective geometry and then in Robotics, such people
do not have any idea about categories (nor on Hopf algebras, but one can
just explaing the algorithm without saying 'Hopf' :).

        Indeed I was pressed several time by maple to do quite nasty
things to keep the type of objects, e.g. to write &t(0) for zero just to
be able to typecheck it being a tensor! Such things would not happen with
AXIOM ! My experience with multiliner algebra, Hopf algebras and quantum
groups is that a serious type system is 75% of the thing to do, so one
more point for Aldor/AXIOM.

        On the other hand, I spend several weeks and looked at the
Internet and asked lots of people at the ACA 2002 in Volos, Greece about
Groebner basis methods for non-commutative algebras (I would also be
interested in the theory of generating functions in non-commutative
variables which is related) but I was not able yet to implement an
algorithm in maple (and that's not maples fault :).

        I could imagine to look closer to Aldor, I have not yet any hint
how to get AXIOM or to use it, but I think together with the Algebra
library Aldor/Algebra = AXIOM, isn't it? For research projects I do not
need any graphical interface.

        I will sign up the mailing list you told me. Bill Page has send me
the Aldor, AXIOM etc web pages which I have visited. (There I got
Aldor/Algebra). However, since my main activity is in research, I cannot
guarantee that I even have enough time to do some reasonable things there.
As you have confessed the learning curve is really high!

        I am trying to do a base free package for Grassmann and Clifford
Hopf algebras now for several times, but it seems as if the mathematics is
not yet fully understood. That is a further problem with such a high
level approach as is issued by AXIOM: You need from the very beginning a
very precise and theoretical idea about the objects (better morphisms) you
want to deal with.

        Rafal is a person for a quick and dirty hack. He wrote several
procedures which I would not have succeeded to write because he went back
to some maple internal abilities which I didn't want to use since it shows
that one has not understand the case at hand. However it worked pretty
fine! I am not sure if I really will be able to convince him to use
something like AXIOM or Aldor (I was not even able to convince him to use
text based code in maple, but he prefers these awkward worksheets which
cannot be transfered from one maple version to the other).  However, I
know that in Rafal's bookshelf is a volume on AXIOM which he got some time
ago when he went with Prof. Lounesto (who died this year unfortunately)
to some conference on computer algebra. I was already then fascinated by
the clear theoretical concept of this system.

        Compared to GINAC, Aldor has a concept. GINAC is just a collection
of C++ library routines which can be used in any C++ program. However I
miss there a theoretical background, the user has to think there to much
on his own, this was the reason for me not to join that thread.

        I spend quite a bit of time on the maple external c interface.
However, as every time with WMI, it was badly documented and the wrappers
generated by maple took all efficiecy away by data translation into
external C compliant code. Maple does not want you to get access to
internal data strcuturs but that would be necessary fro algebraically
operating functions. Hence I was not able to go beyond some numerical
examples.

        All in all, I cannot promise you to develop anything, but I will
certainly keep track of the further development of Aldor (Where to get
AXIOM?) I will also try to do some private experiments, and let's see what
happens...

Thank you for you kind mail, and hope to stay loosely in contact.
best
BF.

% Bertfried Fauser          Fachbereich Physik    Fach M 678
% Universit"at Konstanz     78457 Konstanz        Germany
% Phone : +49 7531 883786   FAX : +49 7531 88-4864 or 4266
% E-mail: address@hidden
% Web   : http://clifford.physik.uni-konstanz.de/~fauser