[net.math.symbolic] An operator algebra for MACSYMA

JPG@MIT-MC.ARPA (11/12/85)

Received: from MIT-MC.ARPA by rand-unix.ARPA; Sat, 9 Nov 85 00:32:38 pst
Date: Sat,  9 Nov 85 03:31:51 EST
From: "Jeffrey P. Golden" <JPG@MIT-MC.ARPA>
Subject: An operator algebra for MACSYMA
Cc: JPG@MIT-MC.ARPA
Message-Id: <[MIT-MC.ARPA].712547.851109.JPG>

(For submission to net.math.symbolic)

   From: watmum!ghgonnet (Gaston H. Gonnet)
   Newsgroups: net.math.symbolic
   Subject: A proposal for operators in Maple
   Date: 31 Oct 85 04:21:33 GMT
   ...
   It is "vox populi" that operators are needed in a symbolic algebra
   system ... During the first Maple retreat (June 11-12, 1983, Research
   Report CS-83-31) we established a basic design for operators.
I too have been working on an operator algebra package, for MACSYMA.
I am happy to learn of your effort, which I was not aware of.  Needless to 
say, there is a large intersection between your design and mine, but many 
differences as well.  I am hoping to submit a paper on my effort to the 
SYMSAC 86 Conference, but I still have some details to work out, so I hope 
I get it done on time.  I'd be happy to discuss things with your group 
when I am further along.

   We found useful to have some "witness" examples that we want to solve 
   in an elegant and general form.  The two main examples were:
   [1] How to represent the first derivative of f(x) at 0
   (the above really refers to the differentiation operator)
   [2] Allow a special "multiplication" operator
   (e.g. non-commutative multiplication)
   Of course many systems solve the above problems, but in some cases
   (in particular for the first example) as an ad-hoc solution, and not
   as a general "operator solution".
I presented my solution to [1] in the May 1985 issue of the SIGSAM 
Bulletin.  (The solution has sinced changed in minor ways.  The Symbolics 
MACSYMA Newsletter(TM) for July 1985 describes the current version.)
I chose an operator solution, indeed I found that to be the best way to 
accurately model the relevant mathematics.  However, obviously you can't 
see how that fits into the rest of my operator algebra scheme at this time.

MACSYMA has long had a non-commutative multiplication operator, the "dot" 
operator, and I use it to represent composition of operators.