MATHLAB 68(ID:3119/mat007)

Second release of MATHLAB 





Related languages
Korsvold => MATHLAB 68   Incorporated some features of
MATHLAB => MATHLAB 68   Evolution of
MATHLAB 68 => MACSYMA   Influence
MATHLAB 68 => REDUCE 2   Incorporated some features of
MATHLAB 68 => Scratchpad   Influence

References:
  • Engelman, C. "MATHLAB 68" pp462-467 view details
          in Morrell, A. J. H. (Ed.): Information Processing 68, Proceedings of IFIP Congress 1968, Edinburgh, UK, 5-10 August 1968 view details
  • Diffie, B. W., and Engelman, C., MATHLAB Project Report, M69-72, The MITRE Corporation, Sept. 1969. view details
          in Morrell, A. J. H. (Ed.): Information Processing 68, Proceedings of IFIP Congress 1968, Edinburgh, UK, 5-10 August 1968 view details
  • Smith, Lyle B. "A Survey of Interactive Graphical Systems for Mathematics" view details Extract: MATHLAB 68
    MATHLAB 68
    Since 1965, MATHLAB has been largely recoded, see Engelman (1968), and is now implemented within a time-sharing system on the large core Digital Equipment Corporation PDP-6 of the Artificial Intelligence Laboratory at Project MAC, MIT. A major improvement to the readability of MATHLAB output is the two-dimensional display program, see Millen (1968), which operates on any typewriter-like device as well as on a variety of scopes and plotters that can be used by MATHLAB. A discussion of the representation, simplification, and use of rational functions and polynomials is given by Manove et al. (1968).

          in [ACM] ACM Computing Surveys 2(4) Dec1970 view details
  • Barton, D. and Fitch, J.P. "General Relativity and the Application of Algebraic Manipulative Systems" view details
          in [ACM] CACM 14(08) August 1971 view details
  • Engelman, C., MATHLAB Manual, M71-103, The MITRE Corporation, Bedford, Mass., 1971. view details
          in [ACM] CACM 14(08) August 1971 view details
  • Engelman, Carl "The Legacy of MATHLAB 68" view details
          in [ACM] Proceedings of the Second Symposium on Symbolic and Algebraic Manipulation, March 23-25, 1971 Los Angeles (SYMSAM 71) view details
  • Tobey, RG "Symbolic mathematical computation - introduction and overview" view details
          in [ACM] Proceedings of the Second Symposium on Symbolic and Algebraic Manipulation, March 23-25, 1971 Los Angeles (SYMSAM 71) view details
  • Sammet, Jean E. "Roster of Programming Languages for 1973" p147 view details
          in ACM Computing Reviews 15(04) April 1974 view details
  • Stock, Marylene and Stock, Karl F. "Bibliography of Programming Languages: Books, User Manuals and Articles from PLANKALKUL to PL/I" Verlag Dokumentation, Pullach/Munchen 1973 365 view details Abstract: PREFACE  AND  INTRODUCTION
    The exact number of all the programming languages still in use, and those which are no longer used, is unknown. Zemanek calls the abundance of programming languages and their many dialects a "language Babel". When a new programming language is developed, only its name is known at first and it takes a while before publications about it appear. For some languages, the only relevant literature stays inside the individual companies; some are reported on in papers and magazines; and only a few, such as ALGOL, BASIC, COBOL, FORTRAN, and PL/1, become known to a wider public through various text- and handbooks. The situation surrounding the application of these languages in many computer centers is a similar one.

    There are differing opinions on the concept "programming languages". What is called a programming language by some may be termed a program, a processor, or a generator by others. Since there are no sharp borderlines in the field of programming languages, works were considered here which deal with machine languages, assemblers, autocoders, syntax and compilers, processors and generators, as well as with general higher programming languages.

    The bibliography contains some 2,700 titles of books, magazines and essays for around 300 programming languages. However, as shown by the "Overview of Existing Programming Languages", there are more than 300 such languages. The "Overview" lists a total of 676 programming languages, but this is certainly incomplete. One author ' has already announced the "next 700 programming languages"; it is to be hoped the many users may be spared such a great variety for reasons of compatibility. The graphic representations (illustrations 1 & 2) show the development and proportion of the most widely-used programming languages, as measured by the number of publications listed here and by the number of computer manufacturers and software firms who have implemented the language in question. The illustrations show FORTRAN to be in the lead at the present time. PL/1 is advancing rapidly, although PL/1 compilers are not yet seen very often outside of IBM.

    Some experts believe PL/1 will replace even the widely-used languages such as FORTRAN, COBOL, and ALGOL.4) If this does occur, it will surely take some time - as shown by the chronological diagram (illustration 2) .

    It would be desirable from the user's point of view to reduce this language confusion down to the most advantageous languages. Those languages still maintained should incorporate the special facets and advantages of the otherwise superfluous languages. Obviously such demands are not in the interests of computer production firms, especially when one considers that a FORTRAN program can be executed on nearly all third-generation computers.

    The titles in this bibliography are organized alphabetically according to programming language, and within a language chronologically and again alphabetically within a given year. Preceding the first programming language in the alphabet, literature is listed on several languages, as are general papers on programming languages and on the theory of formal languages (AAA).
    As far as possible, the most of titles are based on autopsy. However, the bibliographical description of sone titles will not satisfy bibliography-documentation demands, since they are based on inaccurate information in various sources. Translation titles whose original titles could not be found through bibliographical research were not included. ' In view of the fact that nany libraries do not have the quoted papers, all magazine essays should have been listed with the volume, the year, issue number and the complete number of pages (e.g. pp. 721-783), so that interlibrary loans could take place with fast reader service. Unfortunately, these data were not always found.

    It is hoped that this bibliography will help the electronic data processing expert, and those who wish to select the appropriate programming language from the many available, to find a way through the language Babel.

    We wish to offer special thanks to Mr. Klaus G. Saur and the staff of Verlag Dokumentation for their publishing work.

    Graz / Austria, May, 1973
          in ACM Computing Reviews 15(04) April 1974 view details
  • Sammet, Jean E "Roster of programming languages for 1976-77" pp56-85 view details
          in SIGPLAN Notices 13(11) Nov 1978 view details
  • Geddes, K.O. ; Czapor S.R. and G. Labahn, "Algorithms for Computer Algebra" Kluwer Academic Publishers, Boston, 1992 view details Extract: Extract from Chapter one
    A BRIEF HISTORICAL SKETCH
    -------------------------

    The development of systems for symbolic mathematical computation first became
    an active area of research and implementation during the decade 1961-1971.
       . . .
       . . .

    To put the decade 1961-1971 into perspective, let us recall that FORTRAN
    appeared about 1958 and ALGOL in 1960. These two languages were designed
    primarily for numerical mathematical computation.
    Then in 1960/1961 came the development of LISP, a language for list
    processing. LISP was a major advancement on the road to languages for
    symbolic computation. An operation such as symbolic differentiation which
    is foreign to FORTRAN and ALGOL is relatively easy in LISP. (Indeed this
    is one of the standard programming assignments for students first learning
    LISP.) As will be noted later, several computer algebra systems were
    written in LISP.

    1961-1966
    ---------

    In 1961, James Slagle at M.I.T. wrote a LISP program called SAINT
    for Symbolic Automatic INTegration.
    This was one of the earliest applications of LISP to symbolic computation
    and it was the first comprehensive attempt to program a computer to behave
    like a freshman calculus student.
    The program was based on a number of heuristics for indefinite integration
    and it performed about as well as a good calculus student.

    One of the first systems for symbolic computation was FORMAC, developed
    by Jean Sammet, Robert Tobey, and others at IBM during the period 1962-1964.
    It was a FORTRAN preprocessor (a PL/I version appeared later) and it was
    designed for the manipulation of elementary functions including, of course,
    polynomials and rational functions.
    Another early system was ALPAK, a collection of FORTRAN-callable subroutines
    written in assembly language for the manipulation of polynomials and rational
    functions. It was designed by William S. Brown and others at Bell Laboratories
    and was generally available about 1964.
    A language now referred to as Early ALTRAN was designed at Bell Laboratories
    during the period 1964-1966. It used ALPAK as its package of computational
    procedures.

    There were two other significant systems for symbolic computation developed
    during this period. George Collins at IBM and the University of Wisconsin
    (Madison) developed PM, a system for polynomial manipulation, an early
    version of which was operational in 1961 with improvements added to the
    system through 1966. The year 1965 marked the first appearance of MATHLAB,
    a LISP-based system for the manipulation of polynomials and rational
    functions, developed by Carl Engelman at M.I.T. It was the first interactive
    system designed to be used as a symbolic calculator. Included among its
    many firsts was the use of two-dimensional output to represent its
    mathematical output.

    The work of this period culminated in the first ACM Symposium on Symbolic
    and Algebraic Manipulation held in March 1966 in Washington, D.C.
    That conference was summarized in the August 1966 issue of the Communications
    of the ACM.

    1966-1971
    ---------

    In 1966/1967, Joel Moses at M.I.T. wrote a LISP program called SIN
    (for Symbolic Integrator). Unlike the earlier SAINT program, SIN was
    algorithmic in approach and it was also much more efficient.
    In 1968, Tony Hearn at Stanford University developed REDUCE, an
    interactive LISP-based system for physics calculations. One of its
    principal design goals was portability over a wide range of platforms,
    and as such only a limited subset of LISP was actually used.
    The year 1968 also marked the appearance of Engelman's MATHLAB-68,
    an improved version of the earlier MATHLAB interactive system, and of
    the system known as Symbolic Mathematical Laboratory developed by
    William Martin at M.I.T. in 1967.
    The latter was a linking of several computers to do symbolic manipulation
    and to give good graphically formatted output on a CRT terminal.

    The latter part of the decade saw the development of several important
    general purpose systems for symbolic computation.
    ALTRAN evolved from the earlier ALPAK and Early ALTRAN as a language and
    system for the efficient manipulation of polynomials and rational functions.
    George Collins developed SAC-1 (for Symbolic and Algebraic Calculations)
    as the successor of PM for the manipulation of polynomials and rational
    functions. CAMAL (CAMbridge Algebra system) was developed by David Barton,
    Steve Bourne, and John Fitch at the University of Cambridge. It was
    implemented in the BCPL language, and was particularly geared to
    computations in celestial mechanics and general relativity.
    REDUCE was redesigned by 1970 into REDUCE 2, a general purpose system
    with special facilities for use in high-energy physics calculations.
    It was written in an ALGOL-like dialect called RLISP, avoiding the
    cumbersome parenthesized notation of LISP, while at the same time retaining
    its original design goal of being easily portable.
    SCRATCHPAD was developed by J. Griesmer and Richard Jenks at IBM Research
    as an interactive LISP-based system which incorporated significant portions
    of a number of previous systems and programs into its library, such as
    MATHLAB-68, REDUCE 2, Symbolic Mathematical Library, and SIN.
    Finally, the MACSYMA system first appeared about 1971.
    Designed by Joel Moses, William Martin, and others at M.I.T., MACSYMA was
    the most ambitious system of the decade.
    Besides the standard capabilities for algebraic manipulation, it included
    facilities to aid in such computations as limit calculations, symbolic
    integration, and the solution of equations.

    The decade from 1961 to 1971 concluded with the Second Symposium on
    Symbolic and Algebraic Manipulation held in March 1971 in Los Angeles.
    The proceedings of that conference constitute a remarkably comprehensive
    account of the state of the art of symbolic mathematical computation in 1971.

    1971-1981
    ---------

    While all of the languages and systems of the sixties and seventies began
    as experiments, some of them were eventually put into "production use''
    by scientists, engineers, and applied mathematicians outside of the
    original group of developers. REDUCE, because of its early emphasis on
    portability, became one of the most widely available systems of this decade.
    As a result it was instrumental in bringing computer algebra to the attention
    of many new users. MACSYMA continued its strong development, especially
    with regard to algorithm development. Indeed, many of the standard
    techniques (e.g. integration of elementary functions, Hensel lifting,
    sparse modular algorithms) in use today either came from, or were strongly
    influenced by, the research group at M.I.T. It was by far the most powerful
    of the existing computer algebra systems.

    SAC/ALDES by G. Collins and R. Loos was the follow-up to Collins' SAC-1.
    It was a non-interactive system consisting of modules written in the ALDES
    (Algebraic DEScription) language, with a translator converting the results
    to ANSI FORTRAN. One of its most notable distinctions was in being the only
    major system to completely and carefully document its algorithms.
    A fourth general purpose system which made a significant mark in the late
    1970's was muMATH. Developed by David Stoutemyer and Albert Rich at the
    University of Hawaii, it was written in a small subset of LISP and came
    with its own programming language, muSIMP.
    It was the first comprehensive computer algebra system which could actually
    run on the IBM family of PC computers.
    By being available on such small and widely accessible personal computers,
    muMATH opened up the possibility of widespread use of computer algebra
    systems for both research and teaching.

    In addition to the systems mentioned above, a number of special purpose
    systems also generated some interest during the 1970's. Examples of these
    include: SHEEP, a system for tensor component manipulation designed by
    Inge Frick and others at the University of Stockholm;
    TRIGMAN, specially designed for computation of Poisson series and written
    in FORTRAN by W. H. Jeffreys at University of Texas (Austin);
    and SCHOONSCHIP by M. Veltman of the Netherlands for computations in
    high-energy physics.
    Although the systems already mentioned have all been developed in
    North America and Europe, there were also a number of symbolic manipulation
    programs written in the U.S.S.R. One of these is ANALITIK, a system
    implemented in hardware by V. M. Glushkov and others at the Institute of
    Cybernetics, Kiev.

    1981-1991
    ---------

    Due to the significant computer resource requirements of the major
    computer algebra systems, their widespread use remained (with the exception
    of muMATH) limited to researchers having access to considerable
    computing resources. With the introduction of microprocessor-based
    workstations, the possibility of relatively powerful desk-top computers
    became a reality. The introduction of a large number of different computing
    environments, coupled with the often nomadic life of researchers (at least
    in terms of workplace locations) caused a renewed emphasis on portability
    for the computer algebra systems of the 1980's.
    More efficiency (particularly memory space efficiency) was needed in order
    to run on the workstations that were becoming available at this time,
    or equivalently, to service significant numbers of users on the
    time-sharing environments of the day.
    This resulted in a movement towards the development of computer algebra
    systems based on newer "systems implementation'' languages such as C,
    which allowed developers more flexibility to control the use of
    computer resources. The decade also marked a growth in the commercialization
    of computer algebra systems. This had both positive and negative effects
    on the field in general. On the negative side, users not only had to
    pay for these systems but also they were subjected to unrealistic claims
    as to what constituted the state of the art of these systems. However,
    on the positive side, commercialization brought about a marked increase in
    the usability of computer algebra systems, from major advances in user
    interfaces to improvements to their range of functionality in such areas
    as graphics and document preparation.

    The beginning of the decade marked the origin of MAPLE.
    Initiated by Gaston Gonnet and Keith Geddes at the University of Waterloo,
    its primary motivation was to provide user accessibility to computer algebra.
    MAPLE was designed with a modular structure: a small compiled kernel of
    modest power, implemented completely in the systems implementation
    language C (originally B, another language in the "BCPL family'')
    and a large mathematical library of routines written in the user-level
    MAPLE language to be interpreted by the kernel. Besides the command
    interpreter, the kernel also contained facilities such as integer and
    rational arithmetic, simple polynomial manipulation, and an efficient
    memory management system. The small size of the kernel allowed it to be
    implemented on a number of smaller platforms and allowed multiple users
    to access it on time-sharing systems.
    Its large mathematical library, on the other hand, allowed it to
    be powerful enough to meet the mathematical requirements of researchers.

    Another system written in C was SMP (Symbolic Manipulation Program) by
    Stephen Wolfram at Caltech. It was portable over a wide range of machines
    and differed from existing systems by using a language interface that was
    rule-based. It took the point of view that the rule-based approach was the
    most natural language for humans to interface with a computer algebra
    program. This allowed it to present the user with a consistent,
    pattern-directed language for program development.

    The newest of the computer algebra systems during this decade were
    MATHEMATICA and DERIVE.
    MATHEMATICA is a second system written by Stephen Wolfram (and others). It
    is best known as the first system to popularize an integrated environment
    supporting symbolics, numerics, and graphics. Indeed when MATHEMATICA
    first appeared in 1988, its graphical capabilities (2-D and 3-D plotting,
    including animation) far surpassed any of the graphics available on
    existing systems. MATHEMATICA was also one of the first systems to
    successfully illustrate the advantages of combining a computer algebra
    system with the easy-to-use editing features on machines designed to use
    graphical user-interfaces (i.e. window environments). Based on C,
    MATHEMATICA also comes with its own programming language which closely
    follows the rule-based approach of its predecessor, SMP.

    DERIVE, written by David Stoutemyer and Albert Rich, is the follow-up to
    the successful muMATH system for personal computers. While lacking the
    wide range of symbolic capabilities of some other systems, DERIVE has an
    impressive range of applications considering the limitations of the 16-bit
    PC machines for which it was designed.
    It has a friendly user interface, with such added features as two-dimensional
    input editing of mathematical expressions and 3-D plotting facilities.
    It was designed to be used as an interactive system and not as a programming
    environment.

    Along with the development of newer systems, there were also a number of
    changes to existing computer algebra systems. REDUCE 3 appeared in 1983,
    this time with a number of new packages added by outside developers.
    MACSYMA bifurcated into two versions, DOE-MACSYMA and one distributed by
    SYMBOLICS, a private company best known for its LISP machines.
    Both versions continued to develop, albeit in different directions,
    during this decade. AXIOM, (known originally as SCRATCHPAD II)
    was developed during this decade by Richard Jenks, Barry Trager,
    Stephen Watt and others at the IBM Thomas J. Watson Research Center.
    A successor to the first SCRATCHPAD language, it is the only
    "strongly typed'' computer algebra system. Whereas other computer algebra
    systems develop algorithms for a specific collection of algebraic domains
    (such as, say, the field of rational numbers or the domain of polynomials
    over the integers), AXIOM allows users to write algorithms over general
    fields or domains.

    As was the case in the previous decade, the eighties also found a number
    of specialized systems becoming available for general use.
    Probably the largest and most notable of these is the system CAYLEY,
    developed by John Cannon and others at the University of Sydney, Australia.
    CAYLEY can be thought of as a "MACSYMA for group theorists.''
    It runs in large computing environments and provides a wide range
    of powerful commands for problems in computational group theory.
    An important feature of CAYLEY is a design geared to answering questions not
    only about individual elements of an algebraic structure, but more
    importantly, questions about the structure as a whole. Thus, while one
    could use a system such as MACSYMA or MAPLE to decide if an element in a
    given domain (such as a polynomial domain) has a given property (such as
    irreducibility), CAYLEY can be used to determine if a group structure is
    finite or infinite, or to list all the elements in the center of the
    structure (i.e. all elements which commute with all the elements of the
    structure).

    Another system developed in this decade and designed to solve problems
    in computational group theory is GAP (Group Algorithms and Programming)
    developed by J. Neubueser and others at the University of Aachen, Germany.
    If CAYLEY can be considered to be the "MACSYMA of group theory,'' then GAP
    can be viewed as the "MAPLE of group theory.'' GAP follows the general
    design of MAPLE in implementing a small compiled kernel (in C) and a large
    group theory mathematical library written in its own programming language.

    Examples of some other special purpose systems which appeared during this
    decade include FORM by J. Vermaseren, for high energy physics calculations,
    LiE, by A.M. Cohen for Lie Algebra calculations,
    MACAULAY, by Michael Stillman, a system specially built for computations
    in Algebraic Geometry and Commutative Algebra,
    and PARI by H. Cohen in France, a system oriented mainly for number theory
    calculations. As with most of the new systems of the eighties, these last
    two are also written in C for portability and efficiency.

    Research Information about Computer Algebra
    -------------------------------------------

    Research in computer algebra is a relatively young discipline, and the
    research literature is scattered throughout various journals devoted to
    mathematical computation. However, its state has advanced to the point where
    there are two research journals primarily devoted to this subject area: the
    "Journal of Symbolic Computation" published by Academic Press
    and "Applicable Algebra in Engineering, Communication and Computing"
    published by Springer-Verlag.
    Other than these two journals, the primary source of recent research
    advances and trends is a number of conference proceedings.
    Until recently, there was a sequence of North American conferences and
    a sequence of European conferences.
    The North American conferences, primarily organized by ACM SIGSAM
    (the ACM Special Interest Group on Symbolic and Algebraic Manipulation),
    include SYMSAM '66 (Washington, D.C.), SYMSAM '71 (Los Angeles),
    SYMSAC '76 (Yorktown Heights), SYMSAC '81 (Snowbird),
    and SYMSAC '86 (Waterloo).
    The European conferences, organized by SAME (Symbolic and Algebraic
    Manipulation in Europe) and ACM SIGSAM, include the following whose
    proceedings have appeared in the Springer-Verlag series
    "Lecture Notes in Computer Science":
    EUROSAM '79 (Marseilles), EUROCAM '82 (Marseilles),
    EUROCAL '83 (London), EUROSAM '84 (Cambridge),
    EUROCAL '85 (Linz), and EUROCAL '87 (Leipzig).
    Starting in 1988, the two streams of conferences have been merged
    and they are now organized under the name ISSAC (International Symposium
    on Symbolic and Algebraic Computation),
    including ISSAC '88 (Rome), ISSAC '89 (Portland, Oregon),
    ISSAC '90 (Tokyo), ISSAC '91 (Bonn) and ISSAC '92 (Berkeley).


    -----------------------------------------------
    Professor Keith Geddes
    Symbolic Computation Group
    Department of Computer Science
    University of Waterloo
    Waterloo  ON  N2L 3G1
    CANADA
          in SIGPLAN Notices 13(11) Nov 1978 view details