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)

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