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.