In 1970 I encountered a symbolic math program in the standard PDP-10 software distribution called Mathlab (Well, there was a six character proram name limit, so it was invoked, I think, as MATLAB). It identified itself as having been developed at RAND Corp. It could combine expressions and differentiate well, but was weak at integration and equation solving. In 1971, after using Mathlab intensively to derive the light-delayed imagery equations for a relativistic 3D SpaceWar (at Stanford AI Lab) someone (Whit Diffie) told me I was foolish to use it when there was a much further developed version at MIT AI lab called Macsyma (Project MAC (Man And Computer, Machine Aided Cognition, etc.) Symbolic Mathematics -- invoked as MACSYM). I could access it through Telnet over the new ARPAnet! At that time one could just log into the MIT AI PDP-10, running ITS (The "Incompatible Time Sharing" System, whose top level interface was DDT, a debugger), create a new ID for oneself, and access, read, write and delete anybody else's files, as well as making one's own. At the time Macsyma used Joel Moses' thesis SAINT, a heuristic program, for integration. It was OK, but gave up on some integrable functions. The Macsyma group was in the process of implementing a version of the recently discovered Risch algorithm to handle cases that eluded the heuristics. Anyway, I was a happy user of MACSYMA for many, many purposes from then to about 1980, when the MACSYMA group made a half-hearted effort to go commercial, a wing of the new Lisp machine company Symbolics. To meet government contractual obligations, they did distribute a VAX version (VAXIMA) at duplication cost to universities. I used Vaxima from about 1981 to maybe 1987, when the first versions of Steve Wolfram's Mathematica (inspired by but competitive with Macsyma) for Macintosh appeared. I used it for many years, but became convinced through USENET testimonials that the University of Waterloo's MAPLE program had a sounder representation, and produced more reliable results. I've used versions of MAPLE on my Macs since about 1992.
Don Taylor <firstname.lastname@example.org> > I believe that Macsyma predated all of this, was an inspiration > for most of these and was not an offshoot of any of these.
> I believe Mathlab is probably spelled Matlab and was never the > basis for Macsyma but was a numerical linear algebra package > that appeared long after any of these, independently of any of them.