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]> 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]. > 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/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/CAKgW%3D6Jm%2BUq8kdu2gs0C7UxmKVn9ePxjA2f%2BKnHgs6DbiLWhMw%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
