Bill Schelter’s Maxima

Bill Schelter was a remarkable man. First, he was a top-class mathematician. If you allow yourself to be impressed, read his proof of the Artin-Procesi theorem. Bill was also among the first to take non-commutative geometry seriously. Together with Mike Artin he investigated a notion of non-commutative integral extensions and he was the first to focuss attention to formally smooth algebras (a suggestion later taken up by a.o. Cuntz-Quillen and Kontsevich) and a relative version with respect to algebras satisfying all identities of n x n matrices which (via work of Procesi) led to smooth@n algebras. To youngsters, he is probably best know as the co-inventor of Artin-Schelter regular algebras. I still vividly remember an overly enthusiastic talk by him on the subject in Oberwolfach, sometime in the late eighties. Secondly, Bill was a genuine Lisp-guru and a strong proponent of open source software, see for example his petition against software patents. He maintanind his own version of Kyoto Common Lisp which developed into Gnu Common Lisp. A quote on its history :

GCL is the product of many hands over many years. The original effort was known as the Kyoto Common Lisp system, written by Taiichi Yuasa and Masami Hagiya in 1984. In 1987 new work was begun by William Schelter, and that version of the system was called AKCL (Austin Kyoto Common Lisp). In 1994 AKCL was released as GCL (GNU Common Lisp) under the GNU public library license. The primary purpose of GCL during that phase of it’s existence was to support the Maxima computer algebra system, also maintained by Dr. Schelter. It existed largely as a subproject of Maxima.

Maxima started as Bill’s version of Macsyma an MIT-based symbolic computation program to which he added many routines, one of which was Affine a package that allowed to do Groebner-like computations in non-commutative algebras (implementing Bergman’s diamond lemma) and which he needed to get a grip on 3-dimensional Artin-Schelter regular algebras. Michel and me convinced Fred to acquire funds to buy us a work-station (costing at the time 20 to 30 iMacs) and have Bill flown in from the States with his tape of maxima and let him port it to our Dec-station. Antwerp was probably for years the only place in the world (apart from MIT) where one could do calculations in affine (probably highly illegal at the time). Still, lots of people benefitted from this, among others Michaela Vancliff and Kristel Van Rompay in their investigation of 4-dimensional Artin-Schelter regular algebras associated to an automorphism of a quadric in three-dimensional projective space. Yesterday I ran into Bill (alas virtually) by browsing the crypto-category of Fink. There it was, maxima, Bill’s package! I tried to install it with the Fink Commander and failed but succeeded from the command line. So, if you want to have your own version of it type

sudo fink
install maxima

from the Terminal and it will install without problems (giving you also a working copy of common lisp). Unfortunately I do not remember too much of Macsyma or Affine but there is plenty of documentation on the net. Manuals and user guides can be obtained from the maxima homepage and the University of Texas (Bill’s university) maintains an online manual, including a cryptic description of some Affine-commands. But probably I’ll have to send Michaela an email asking for some guidance on this… Here, as a tribute to Bill who died in july 2001 the opening banner

 iMacLieven:~ lieven$
/sw/bin/maxima Maxima 5.9.0 http://maxima.sourceforge.net 
Distributed under the GNU Public License. 
See the file COPYING. 
Dedicated to the memory of William Schelter. 
This is a development version of Maxima. 
The function bug_report() provides bug reporting information. 
(C1)