History of CA Systems evans@eedsp.gatech.edu (Brian Evans) Georgia Institute of Technology --> Introduction The roots of computer algebra apparently go all the way back to the 1950's. In the 1960's, three primary groups launched into the field-- mathematicians, physicists, and AI researchers. The first two groups created several special purpose environments. For example, mathematicians created Cayley for group theory and SAC for cylindrical decomposition, whereas physicists produced SHEEP for relativity and MAO for celestial mechanics. REDUCE evolved from a program to do computational physics into a general computer algebra system. Many AI researchers were laying the groundwork for MACSYMA during this time, as is evident from the work by the MathLab group at MIT and by The MITRE Corporation (who wrote the MATHLAB program). The 1960's saw other work in the field. Bell Labs produced ALPAK (1964) and its successor ALTRAN (1966). IBM produced FORMAC, Scratchpad, Scratchpad II, and Axiom. (IBM recently assigned the copyright of Axiom, a distant relative of Scratchpad, to the Numerical Algorithms Group Ltd.) MACSYMA came together in 1970 and is the father of many popular computer algebra systems today. Until the late 1970's, however, MACSYMA only ran on mainframe computers, although one mainframe (the DEC PDP-10) required a special purpose operating system. With the advent of personal computing in 1977, attempts were made to write a computer algebra program for these small computers. The first commercial success for these small platforms was muMath (1979). In the 1980's, a host of programs for the PC were released, including a port of Maple to the IBM PC in the late 1980's. In 1982, MIT granted Symbolics Inc. the right to develop MACSYMA and by 1989 had ported it to personal computers (although there was a version running on 8 Mb 68000 Pixel Corp computer at Berkeley c. 1982). Mathematica, another popular environment, was released in 1988 for Macintosh computers. PowerMath, the first computer mathematics environment for the Macintosh, was on the market in 1985. Today, the computer algebra systems on the market typically run on several different platforms, including personal computers, workstations, and mainframes. --> Summary Here are the dates (or approx. dates) when many of the key general purpose computer algebra systems were released (after Beta testing): ^^^^^^^^ ^^^^ Environment Release Derivative Works e-mail ad. or phone no. --------------- -------- --------------------- ----------------------- ALPAK 1964 ALTRAN (Bell Labs) ALTRAN 1968 (Bell Labs) FORMULA (Algol). FORMAC FORMAC (PL/I) (IBM) FORMAC (PL/I) (IBM) MATHLAB (DECUS) 1968 MACSYMA (DEC) CAMAL *REDUCE 1968 reduce-netlib@rand.org **MACSYMA 1970 Symbolics Macsyma, (See Below) VAXIMA, DOE-Macsyma, ALJABR, ParaMacs *SchoonShip 1971 archive.umich.edu (FTP) muMath 1979 Derive ***VAXIMA 1980 (312) 972-7250 ****SMP 1982 Mathematica NOT ON MARKET Symbolics MACSYMA 1983 macsyma-service@symbolics.com ***DOE-Macsyma 1984 ALJABR gcook@llnl.gov Maple 1985 wmsi@daisy.waterloo.edu *****MathCAD 1985 (?) Mathcad 1-800-MATHCAD Powermath 1985 NOT ON MARKET *REDUCE/PC 1986 reduce-netlib@rand.org Derive 1988 (Soft Warehouse Inc.) Mathematica 1988 info@wri.com Theorist 1988 (415) 543-2252 (Prescience Corp) PARI 1988 (?) ftp to math.ucla.edu FORM 1989 form@can.nl MACSYMA/PC 1989 macsyma-service@symbolics.com ALJABR 1991 aljabr@fpr.com Mathcad 1991 1-800-MATHCAD SymbMath 1991 chen@deakin.oz.au Axiom 1991 (708) 971-2337 ParaMacs 1991 lph@paradigm.com SIMATH 1992 marc@math.uni-sb.de * Some would claim that the original release of REDUCE (1968) shared some similarities with Ashmedai (never marketed) and SchoonSchip (1971) because they were begun at about the same time (1963). Originally, REDUCE was implemented in Lisp and SchoonSchip in CDC assembler, so their interfaces and command syntax are quite different. Subsequently, they evolved in dramatically different directions. Also, when mailing for information about REDUCE, entitle the e-mail message `send info-package`. For questions requiring a human response, send e-mail to "reduce@rand.org". ** MACSYMA has certainly influenced most if not all of the symbolic mathematics environments released after 1971. In fact, some of the implementors of MACSYMA have helped write other platforms (e.g., Barry Trager / Scratchpad, David Stoutemeyer / Derive, Bruce Char / Maple, and Steve Wolfram / Mathematica). MIT has licensed a handful of companies to develop MACSYMA: Symbolics Inc., Intermath, DOE, Fort Pond Research, and Paradigm Associates Inc., the first being Symbolics Inc. in 1982. This accounts for the many derivations. *** VAXIMA was ready for full release in the early 1980's but the exclusive licensing agreement between MIT and Symbolics Inc. in 1982 put the legality of this into question. VAXIMA was officially released on a large scale in 1988, but full versions were available in universities as early as 1980. A version of DOE-MACSYMA for the Vax under VMS was available in 1984. VAXIMA is available from the National Energy Software Center. **** Actually, its full release was held up after 1982 because of lengthy contractual negotiations between its developer (Dr. Wolfram), CalTech (place where it was developed), and Computer Mathematics Corp. (CMC, which merged later into Inference Corp., was to market SMP). The end results were that SMP was marketed in 1983 and Dr. Wolfram left CalTech. ***** Originally, MathCAD was a numerical processing environment similar to MatLab but with a better user interface. In 1991, MathCAD 3.0 emerged with a new spelling (Mathcad) and symbolic manipulation capabilities (based on Maple). MathCAD and Mathcad are trademarks of MathSoft, Inc. Matlab is a trademark of The Math Works Inc. --> About the Table Certainly, some key computer algebra environments (esp. early ones) were never "released" to the public. For example, the 1965 version of Mathlab (a predecessor of Mathlab '68 and Macsyma) ran only on PDP-6/PDP-10 computers under MIT's ITS timesharing system. Other early systems of note are Scratchpad (1966), PM/SAC/SAC-2, and ALDES. Scratchpad is IBM's in-house software, with two indirect successors Scratchpad II (1975) and Axiom (1991). Axiom is the only one that has been released. Similarly, it was difficult to place a date on the early systems that were "released". For example, SMP and VAXIMA were caught up in legal disputes which delayed their large scale release. In these two cases, I have cited the years in which full releases were available to colleges and universities. In the above list, I have also omitted some of the special purpose systems like SHEEP (relativity), MAO (celestial mechanics), Cayley (group theory), and GAP (group theory). SAC is considered special purpose because it concentrates on algebraic computation with polynomials especially cylindrical algebraic decompositions; however, developers in Austria are working on an interactive front end and a symbolic integrator for SAC-2. I have also excluded TK!Solver (by Universal Technical Systems) from the list because it is a constraint-based numerical solver instead of a symbolic math environment. --> References from N. Soiffer: @INBOOK{ca-applications, AUTHOR = "J. A. van Hulzen and J. Calmet", TITLE = "{Computer Algebra Symbolic and Algebraic Computation}", CHAPTER = "Computer Algebra Applications", PUBLISHER = "Springer-Verlag", EDITION = "Second", YEAR = 1983 } @INPROCEEDINGS{fitch-applications, AUTHOR = "J. Fitch", TITLE = "{A Survey of Symbolic Computation in Physics}", BOOKTITLE = "{Symbolic and Algebraic Computation, Proc. EUROSAM '79}", SERIES = "Lecture Notes in Computer Science 72", YEAR = 1979, PAGES = "30--41", PUBLISHER = "Springer-Verlag", } @INPROCEEDINGS{ng-applications, AUTHOR = "E. Ng", TITLE = "{Symbolic-Numeric Interface: A Review}", BOOKTITLE = "{Symbolic and Algebraic Computation, Proc. EUROSAM '79}", SERIES = "Lecture Notes in Computer Science 72", YEAR = 1979, PAGES = "330-345", PUBLISHER = "Springer-Verlag", } --> Reference from Glenn Thobe R.G. Tobey, R.J. Bogbrow, and S.N. Zilles, {Proc. Amer. Soc. Info. Proc. Soc.}, _27_, 37. (1965), R.G. Tobey, {IBM Technical Report 00.1365} (1965), J.E. Sammet, {Adv. Comp.}, _8_, 47 (1966), W.H. Jeffreys, {Comm. Assoc. Comp. Mach.}, _14_, 538 (1971), M.S. Davis, in B.D. Tapley and V. Szebehely, Eds., {Recent Advances in Dynamical Astronomy}, D. Reidel Publ., Dordrecht, Holland, 1973, p. 351 (1973), R. Pavelle, M. Rothstein, and J. Fitch, {Sci. Am.}, _245_, 136 (1981). --> Other references: Caviness, B. "Computer Algebra : Past and Future." EUROCAL'85, Buchberger, B. (ed). Pages 1-18. Barton and Fitch in {Reports on Progress in Physics} vol. 35, no. 2. G. Gonnet and D. Gruntz. "Algebraic Manipulation: Systems" in the {Encyclopedia of Computer Science and Engineering}, 3rd ed., Ralston, Reilly, and Dahlin eds., Van Nostrand Reinhold, 1991. D. Harper, C. Wooff, and D. Hodgkinson, {A Guide to Computer Algebra Systems}, John Wiley and Sons. ISBN 0-471-92910-7. D. R. Stoutemeyer, ``Crimes and misdemeanors in the computer algebra trade'', Notices of the AMS, Sept. 1991, pp. 701-785. --> Contributors: Doug Andersen hari@sugar.neosoft.com (Axiom) Bill Beckner beckner@math.utexas.com George Carrette gjc@mitech.com (MACSYMA) Bruce Char bchar@mcs.drexel.edu (early sys) Elizabeth Chelkowska ryba@tasman.cc.utas.edu.au (PowerMath) Brian Evans evans@eedsp.gatech.edu Paul Evans pdevans@sail.uwaterloo.ca (Maple/Mathcad) Richard Fateman fateman@peoplesparc.berkeley.edu (MACSYMA etc.) Stuart Feldman sif@lachesis.bellcore.com (ALPAK/ALTRAN) Dan Frezza dfrezza@vela.acs.oakland.edu (Derive) Jeffrey Golden jpg@allegheny.scrc.symbolics.com (MACSYMA) Jeff Greif jmg@inference.com (SMP) Leo Harten lph@paradigm.com (ParaMacs) Tony Hearn hearn@rand.org (REDUCE) Daniel Lazard dl@posso.ibp.fr (Axiom) Michael Monagan mbmonaga@daisy.waterloo.edu (Maple) James O'Dell jim@fpr.com (TK!Solver) Geert Oldenborgh t19@nikhef.nl (SchoonSchip) Ue-Li Pen upen@astro.princeton.edu Richard Pavelle rp@xn.ll.mit.edu Andrzej Pindor pindor@gpu.utcs.utoronto.ca (MathCAD) Mohammed Rayes rayes@mcs.kent.edu Richard Schroeppel fermat!r@la.tis.com Joel Shapiro shapiro@jashap.rutgers.edu Neil Soiffer soiffer@wri.com (Mathematica) Glenn Thobe getunx!thobe@uunet.uu.net (early sys) Jos Vermaseren t68@nikhef.nl (FORM) David Williams dnw@williams.physics.lsa.umich.edu (SchoonShip) Edward Wright Edward_D_Wright@cup.portal.com -- Brian L. Evans Digital Signal Processing Laboratory School of Electrical Engineering Georgia Institute of Technology Atlanta, GA 30332-0250 USENET: ...!{allegra,hplabs,ulysses}!gatech!eedsp!evans INTERNET: evans@eedsp.gatech.edu