Conference rusure::math

15.0. "Tools for Symbolic Math" by HARE::STAN () Mon Jan 23 1984 15:01

     Subj: Tools for Symbolic and Interactive Mathematics            Page 2


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     | d i g i t a l |   I n t e r o f f i c e    M e m o r a n d u m
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     To:                            Date:  23 January 84
     BBM Interest list              From:  Lynn Yarbrough
                                    Dept:  Commercial Languages and Tools
                                    DTN:   381-2205 Loc:  ZKO2-3/K06
                                    File:  symmath.rno
                                    Memo: Not Used  Rev: 0






     In the process  of  planning  the  BlackBoard  Math  project,  I  have
     accumulated  a  number  of tools for mathematical problem solving that
     might be useful to other people.  I have also  experimented  with  the
     use of these tools in an environment in which the tools are invoked as
     Spawned Processes under VMS, and do  thir  I/O  through  Mailboxes  or
     Pipes  (using  the  Pipe  Driver  supplied  by  Paul  Winalski).  This
     environment  can,  in  many  instances,  permit  building  a  stylized
     interface  for  an  existing program without making any changes in the
     program.  However, my tests have revealed some  restrictions  in  this
     mode  of operation which are worth sharing.  I have therefore prepared
     the list of tools and their  special  capabilities  and  restrictions,
     which  appears on the following pages, so that others might be able to
     profit from them.

     Subj: Tools for Symbolic and Interactive Mathematics            Page 3


     BCAL

     This program is a 'desk calculator' type of  tool  which  has  integer
     arithmetic and Boolean logic capability.  I wrote it a couple of years
     ago in BLISS to help in the DIAMOND  work.   It  is  included  in  the
     Software Tools Clearinghouse.

     This program does not work in the spawned environment using pipes.  It
     uses  TUTIO,  the Tutorial BLISS I/O Package that is introduced in our
     BLISS programming Courses, and TUTIO will  not  work  with  Mailboxes.
     This  is  a  restriction  which  it  would  be  well to correct.  I am
     presently replacing the TUTIO interface with an XPORT version, which I
     expect to work OK using pipes.



     CALX

     This program is a 'Programmable Desk Calculator', written by Tom  Hood
     in  FORTRAN.   This  is a much bigger program than BCAL, with a lot of
     FORTRAN  features  (REAL  and   BOOLEAN   operations,   transcendental
     functions,  etc.)  and  interactive  programability.  Documentation is
     reasonable.  It is in the Software Tools Clearinghouse.

     The most recent version(s) of CALX will run in a pipe environment,  if
     the supplied I/O routines are replaced.  Having succesfully done that,
     we are evaluating CALX as a candidate 'back-end' system  for  the  BBM
     project.



     MASS-11

     MASS-11 is a Word Processing  System  which  features  the  use  of  a
     Scientific Character Set including Integral and Summation signs, Greek
     alphabet, etc.  It runs on VAX under VMS and requires a Character  Set
     ROM  for  both the VT100 terminal (which I have) and the LA100 printer
     (which we don't have yet).   I  don't  like  the  user  interface  for
     MASS-11   but   it   has  some  very  interesting  capabilities.   The
     documentation is reasonable and readily available.

     MASS-11 does not work in a pipe environment because  of  the  terminal
     I/O,  which  uses  the full capability of the VT100 and is clearly not
     mailbox-adaptable.



     MACSYMA/VAXIMA

     MACSYMA is a very large (2.5  megabytes  executable  image)  and  well
     documented   symbolic   mathematics   system   which  has  been  under
     development for a number of years at MIT.   In  a  sense,  it  is  the
     benchmark  by  which  other Symbolic Mathematics systems are compared.
     The VAX version is available on the market for about $25000.  We  have
     an  ancient  sub rosa copy of VAXIMA which is buggy but with which one

     Subj: Tools for Symbolic and Interactive Mathematics            Page 4


     can solve some significant problems.  Although written in LISP, VAXIMA
     uses a C I/O library for I/O.

     VAXIMA will not run in a pipe environment.  In this case  the  culprit
     is  the  UNIX  C  I/O  system  which is used, which like TUTIO was not
     designed for a Mailbox application.



     PICOMATH

     A 'toy' Symbol Mathematics system, PICOMATH is written  in  BASIC  and
     will  run on almost anything, certainly on a PDT.  It consists of four
     independent programs, each  of  which  does  symbolic  transformations
     (including  formal  integration and differentiation) of a very limited
     class  of  expressions.   Example:   given  an   arbitrarily   complex
     representation  of  a  function  which  is formally representable as a
     quotient of two polynomials of degree <= 8, the RATIONAL program  will
     recover  the latter representation.  Each of the four programs is less
     than 3 pages long.  For its size, it will do some amazing things,  but
     PICOMATH  is  sharply limited in that, for example, there is no way of
     extending the degree beyond 8.  All four of the programs have  similar
     kinds of limitations.

     PICOMATH will run in a  pipe  environment  in  conjunction  with  VERY
     recent  versions  of  BASIC (earlier versions crash!) It is reasonably
     well documented and easy to use.



     SAC-2

     SAC-2 is a symbolic math system  written  in  FORTRAN  which  is  thus
     largely   transportable   to   many  systems.   It  is  not,  however,
     interactive.  It supports the  writing  of  algorithms  in  ALDES,  an
     ALgorithm  DEScription  language,  and has an immense library of ALDES
     programs to perform mathematical tasks in symbolic  form.   The  ALDES
     translator  produces  FORTRAN  source  as  its  output,  which  can be
     compiled into an efficient running program.  Several examples of SAC-2
     solutions  of  tough  problems  are  available.   The documentation is
     plentiful but not all it should be; a SAC-2 User's Guide mentioned  in
     the literature does not actually exist.

     I have not used SAC-2 beyond verifying that it runs on  test  problems
     supplied by the implementer.



     SMP

     The Symbol Mathematics Program, SMP, is the heir apparent  to  MACSYMA
     as  the  standard  for  symbolic  math  systems in the future.  It has
     features and capabilities which make it roughly equivalent to MACSYMA,
     but  it  is  implemented  in  C  and  therefore  4-20 times as fast as
     MACSYMA.  DEC is jointly promoting SMP with its implementers (at about

     Subj: Tools for Symbolic and Interactive Mathematics            Page 5


     $35000  a  crack)  for  VAX/VMS.   A  SMP  system will be available on
     GOLD::MKT782::  shortly.

     SMP may have the identical problems as VAXIMA in a  pipe  environment.
     We  have  some  hope, though, of getting the I/O interface changed for
     SMP.



     TK!Solver

     TK!Solver runs on a PRO  300  and  is  a  friendly  tool  for  solving
     moderately  large  systems  of equations reasonably quickly.  While it
     has  no  symbolic  capability,   it   permits   very   straightforward
     presentation of the problem equations and related data and can present
     its results in graphical  form  if  appropriate.   It  uses  iterative
     solution    methods    and   linear   interpolation   techniques   for
     representation of user functions.  It is a  good  practical  tool  for
     solving  many  moderately difficult problems.  We have, however, found
     some apparently straightforward problems in  nonlinear  equations  for
     which TK!solver falls flat on its face.

     We have no plans for using TK!Solver in a VAX environment.



     muMATH

     I have recently received a copy of muMath.  It is available  for  CP/M
     systems  including  ROBIN,  PRO 300 and RAINBOW.  muMATH is perhaps as
     full-blown a symbolic math system as will fit in a  personal  computer
     environment.   There  is  no  plan  for a VAX implementation that I am
     aware of.  I have not yet had a chance to run it (on our Robin).