I would not think it was "the first CAS"... but maybe the first at something..
There were quite a few systems way back then. A big conference with lots of system descriptions in papers was held in 1966. The structure of the Lisp simplifier written by Knut Korsvold (circa 1963) is still in Maxima. The rather more sophisticated systems by William A. Martin and Joel Moses came just a bit later (1966 or so). Their theses include source code. But there were others from that time like FORMAC (August, 1962) http://dl.acm.org/citation.cfm?id=807969 and there was also Reduce and CAMAL Schoonschip had a particular niche and was successful in it. As an inspiration for other 'CAS' implementers, I think it fell way short of what Veltman believed to be the case. Running initially on CDC computers, written in assembler, and aimed at problems where sorting of large numbers of terms was critical, it probably could do computations that no other system could do. On the other hand, all numbers were (still are?) machine floats. And Veltman was not keen on notions like "user-friendly" interfaces. On Friday, February 6, 2015 at 11:07:25 AM UTC-8, Aaron Meurer wrote: > > That's very cool. > > It's worth pointing out that John McCarthy's original 1960 LISP paper > (http://www-formal.stanford.edu/jmc/recursive.html) shows how to take > what are effectively symbolic derivatives: > > Our differentiation formula, which gives the derivative of y with > respect to x, is > > diff [y; x] = [atom [y] → [eq [y; x] → ONE; T → ZERO]; eq [car [Y]; > PLUS] → cons [PLUS; maplist [cdr [y]; λ[[z]; diff [car [z]; x]]]]; > eq[car [y]; TIMES] → cons[PLUS; maplist[cdr[y]; λ[[z]; cons [TIMES; > maplist[cdr [y]; λ[[w]; ¬ eq [z; w] → car [w]; T → diff [car [[w]; > x]]]]]]] > > The derivative of the expression (TIMES, X, (PLUS, X, A), Y), as > computed by this formula, is > > (PLUS, (TIMES, ONE, (PLUS, X, A), Y), (TIMES, X, (PLUS, ONE, ZERO), > Y), (TIMES, X, (PLUS, X, A), ZERO)) > > Aaron Meurer > > > On Fri, Feb 6, 2015 at 12:54 PM, Ondřej Čertík <[email protected] > <javascript:>> wrote: > > Hi, > > > > I just found full source codes of perhaps the first computer algebra > > system (CAS) ever, Schoonschip from 1963 by M. Veltman [1] (and > > improvements later by other people), that's 52 years ago: > > > > http://www-personal.umich.edu/~williams/archive/schoonschip/index.html > > > > See the source code: > > > > > http://www-personal.umich.edu/~williams/archive/schoonschip/SchipSrc-CR.tar.gz > > > > > written in assembly language... Moore info about the code: > > > > http://www-personal.umich.edu/~williams/archive/schoonschip/README.txt > > > http://www-personal.umich.edu/~williams/archive/schoonschip/README-src.txt > > > > And a detailed manual: > > > > http://www-personal.umich.edu/~williams/archive/schoonschip/schipman.pdf > > > > The manual is especially interesting to see how the program was used > > and what features it had, and it has lots of info how to implement > > tensors, gamma matrices etc. in particle physics. I think there is > > lots of stuff to learn from it, I am going to read it carefully. > > > > Veltman himself talks about the code on the page 4 at [2]. > > > > Ondrej > > > > [1] http://en.wikipedia.org/wiki/Martinus_J._G._Veltman > > > > [2] > http://www.nobelprize.org/nobel_prizes/physics/laureates/1999/veltman-lecture.pdf > > > > > -- > > You received this message because you are subscribed to the Google > Groups "sympy" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to [email protected] <javascript:>. > > To post to this group, send email to [email protected] > <javascript:>. > > Visit this group at http://groups.google.com/group/sympy. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CADDwiVAqbWpmyDaUbrT1W70piTOf8Vb2E-K-Cu8WPBDS%3DO0nGw%40mail.gmail.com. > > > > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/2ad325ae-3fcf-4653-bc8a-019500615632%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
