Network Working Group W. Parrish
Request for Comments: 525 J. Pickens
NIC: 17161 Computer Systems Laboratory -- UCSB
1 June 1973
MIT-MATHLAB MEETS UCSB-OLS:
An Example of Resource Sharing
I. Introduction
A. Resource Sharing, A Comment
Non-trivial resource sharing among dissimilar system is a much
discussed concept which, to date, has seen only a few real
applications. [See NIC 13538, "1972 Summary of Research
Activities (UTAH) for description of Tony Hearn's TENEX-CCN
Programming Link.] The first attempts have utilized the most
easily accessible communication paths, (TELNET and RJS) and the
most universal representations of numbers (byte-oriented numeric
characters in scientific notation). Future schemes will probably
be more efficient through standardized data and control protocols,
but even with the existing approaches users are gaining experience
with combinations of resources previously not available.
B. The MATHLAB/UCSB-OLS Experiment
MATHLAB [1] and OLS are powerful mathematics systems which cover
essentially non-intersecting areas of mathematical endeavor.
MATHLAB (or MACSYMA) contains a high-powered symbolic manipulation
system. OLS is a highly interactive numeric and graphics system
which, through user programs, allows rapid formulation and
evaluation of problem solutions. Prior to this experiment, users
have dealt with problems symbolically on MATHLAB or numerically
and graphically on OLS. Lacking an interconnecting data path,
users have been left to pencil and paper translation between the
two systems.
The goal of the MATHLAB-OLS experiment is to provide an automated
path whereby expressions at MATHLAB may be translated into User
Programs at UCSB. Thus the user is able to experiment freely with
the numeric, graphic, and symbolic aspects of mathematic problems.
II. THE RESOURCES
To understand this particular case of resource sharing, it is first
necessary to understand, to some degree, the resources being shared.
This paper does not attempt to deal with all of the resources
Parrish & Pickins [Page 1]
RFC 525 MIT-MATHLAB MEETS UCSB-OLS 1 June 1973
available at both sites (UCSB and MIT). Only the applicable shared
resources are discussed briefly. In the section discussing
possibilities for additions (Section V) some available unshared
resources are presented, along with their possible shared
applications. The current implementation is limited to evaluation of
real functions. A description of the capabilities at the two sites
follows.
A. Graphical and Numeric Computation Capabilities at UCSB
To get a graph of a function on the OLS, it is necessary only to
specify the function with a series of button-pushes. For example,
to get a plot on sin(x), the "program"
II REAL SIN x DISPLAY RETURN
will display a plot of sin(x) versus X, provided that X has been
defined as a vector containing values over the range which it is
desired to plot. For a more complete description of OLS see NIC
5748, "The OLS User's Manual". Programs in OLS, or sequences of
button-pushes can be stored under USER level keys, i.e. the above
program could be defined as USER LI (+) [2], and the user could
display, modify, and look at various values of the SIN function
over different ranges by simply setting up the desired value of
the the vector X, and then typing USER LI (+). The number of
elements in such a vector is variable, up to a maximum of 873
(default value is 51). The vector containing the result can be
stored under a letter key, i.e. Y, and can be looked at by typing
DISPLAY Y.
Scaling of plots on the OLS is automatic for best fit, or can be
controlled. Upon default, however, it is often desirable to look
at plots of several functions on a common scale. This can be done
on the OLS, and the graphs will be overlayed. OLS graphical
capabilities are available to users at UCSB on the Culler-Fried
terminals, and to Network users using a special graphics socket at
UCSB. See NIC 15747, RFC 503 "Socket Number List". For Network
users without Culler-Fried keyboards, see NIC 7546, RFC 216
"TELNET Access to UCSB's On-Line System".
B. Symbolic Manipulations Available at MATHLAB
MATHLAB'S MACSYMA provides the capability to do many symbolic
manipulations in a very straightforward and easy-to-learn manner.
Included in these manipulations are:
1) Symbolic integration and differentiation of certain
functions.
Parrish & Pickins [Page 2]
RFC 525 MIT-MATHLAB MEETS UCSB-OLS 1 June 1973
2) Solutions to equations and systems of equations.
3) Laplace and inverse-Laplace transforms of certain functions
4) Certain series expansions.
5) Rational simplification of rational functions.
For a more complete description, see "The MACSYMA User's Manual" by
the MATHLAB Group at Project MAC-MIT.
III. A DESCRIPTION OF THE CURRENT IMPLEMENTATION
A variety of programs are used to make up a system to effect this
transfer of data.
1) Two functions are defined in Lisp-like language which are
loaded into MACSYMA after login in order to facilitate saving a
list of expressions to retrieve later to UCSB, and to write
this list out to a disk file at MATHLAB for later retrieval.
2) A set of OLS user programs create the batch job which actually
performs the retrieval, translation, and storage of these
expressions on a specified file on some OLS user directory.
3) The program which actually performs the connection to MATHLAB
retrieves the expressions, translates and stores into the OLS
is written in PL/1 and exists as a load module on disk at UCSB.
The sequence of operations required in order to retrieve expressions
using these various programs is outlined below:
1) The user makes a connection to MIT-MATHLAB in the conventional
manner. This can be done either through UCSB-OLS, or through
other TELNET programs, or from a TIP.
2) The user logs in at MATHLAB, calls up MACSYMA, and loads the
file into the MACSYMA system which facilitates retrieval.
(Contains ADDLIST and SAVE functions.)
3) The user performs the desired manipulations at MATHLAB, and
saves up a list of line numbers as he goes along using the
ADDLIST function. These line numbers represent those
expressions he wishes to retrieve. The format for ADDLIST is
ADDLIST('<LINE NUMBER>).
Parrish & Pickins [Page 3]
RFC 525 MIT-MATHLAB MEETS UCSB-OLS 1 June 1973
4) When the user has completed all the manipulations he wishes to
do he saves them on the MIT-MATHLAB disk. (Using SAVE
function.) The format for SAVE function is SAVE(<filename 1>).
This function writes out, in horizontal form, the list of line
numbers in the order the ADDLIST function was invoked to the
MIT disk. The filename will be <filename 1>BATCH. SAVE also
appends a question mark on the end of the file as an end-of-
file indicator.
5) USER disconnect from MATHLAB.
6) User connects to and logs into OLS, and loads a file containing
the user programs which produce a virtual job deck for the
batch system. A sequence of questions are given to the user by
these programs regarding accounting information, and the source
file at MIT, and the destination file at at UCSB. The batch
job gets submitted automatically, and the transfer and
translation is done.
7) After the transfer is completed, the destination file may be
loaded into OLS, and the results may be displayed and numerical
manipulations can take place.
The form of these user programs, as they are returned is as follows:
LII REAL LOAD ( function )
Therefore in order to look at a graph of one of these functions, it
is necessary to set up values of various constants, as well as a
range of values of the independent variable. It is also necessary to
request a display of the function. This can be done by typing
DISPLAY RETURN. It should be noted that the function does exist at
the time directly after the user program is called and may be stored
under any of the alphabetical keys on the OLS. Storing several of
these functions under alphabetical keys will allow them to be called
up for plotting on a common scale. For example, if the functions
were stored under the keys A, B, and C, they could be displayed on a
common scale by typing DISPLAY ABC RETURN.
IV. LIMITATIONS
A. The program as it stands can only transfer expressions.
Equations or functions are not implemented.
B. Variable and constant names at MIT can contain more than one
letter, but the current implementation recognizes only one-
letter variable names.
Parrish & Pickins [Page 4]
RFC 525 MIT-MATHLAB MEETS UCSB-OLS 1 June 1973
C. The program as it stands does not handle complex numbers.
D. The user is subject to failures of three independent systems in
order to complete the transfer: the UCSB 360/75, the Network,
and the PDP-10 at MIT. This has not proven to be a serious
constraint.
E. Software changes at either site can cause difficulties since
the programs are written assuming that things won't change.
Anyone who has ever had a program that works knows what system
changes or intermittent glitches can do to foul things up.
With two systems and a Network things are at least four times
as difficult. Thanks are due to Jeffrey Golden at PROJECT MAC
for helping with ironing things out at MATHLAB, and the UCSB
Computer Center for their patience with many I/O bound jobs.
V. POSSIBILITIES FOR ADDITIONS
A. Recognition of complex numbers, possibly for use with LII
COMPLEX on the OLS.
B. Addition to translation tables of WMPTALK for recognition of
SUM, COSH, SINH, INTEGRATE, DIFF, etc. (Often MATHLAB will not
be able to perform an integral or derivative, in which case it
will come back with INTEGRATE (Expression) as its answer.)
C. An OLS Utilities package for allowing users to more easily
manipulate the numerical vectors describing the
expressions,i.e., setting up linear and logarithmic sweeps for
the various plots, describing the scale of the plots on the OLS
screens.
D. The ability to have an OLS program written from a MATHLAB
function, including IF, THEN, ELSE, DO,etc. This would most
likely require a more sophisticated parse than is done in the
current implementation.
EXAMPLE
An example is included in which a UCSB user:
A. Logs into MATHLAB,
B. Initializes the "SAVE" function,
C. Generates a polynomial function and its derivative and
integral,
Parrish & Pickins [Page 5]
RFC 525 MIT-MATHLAB MEETS UCSB-OLS 1 June 1973
D. Logs out of MATHLAB,
E. Creates the retrieval job,
F. Waits and then displays the resultant user programs,
G. and, finally, creates the X variable and plots the functions.
Although the sample OLS manipulations are very simple ones it should
be noted that the user could compare the retrieved functions with
numerical models or even use the functions as subroutines in higher
level algorithms. Usage of this combined numeric-symbolic system is
limited to the imagination of the user.
The example follows:
USER TELNET Connection to MATHLAB from UCSB
LOGIN TO MIT-ML "II LOG MIT-ML RETURN"
JOB TO RETRIEVE MATHLAB
EXPRESSIONS IS NOW IN
UCSB-MOD75 BATCH QUEUE. Some time elapses and batch job is run.
Load the retrieved program.
WORK AREAS UPDATED "SYST LOAD demo11 RETURN"
LOAD demo11
FILE LOADED
Parrish & Pickins [Page 8]
RFC 525 MIT-MATHLAB MEETS UCSB-OLS 1 June 1973
Display the returned expressions.
(USER LI (+)) "USER I DISPLAY (+)"
------------------------------------------------------------------
LII REAL LOAD ((X**2 (+) 3)/(X (+) 1)):
(USER LI (-)) "USER I DISPLAY (-)"
LII REAL LOAD ((X**2 (-) 2*X)/2 + 4* LOG (X (+) 1)):
------------------------------------------------------------------
(USER L1 (*)) "USER I DISPLAY (*)"
LII REAL LOAD (2*X/(X (+) 1) <> (X**2 (+) 3)/(X (+) 1)**2):
USER LI SQ UNDEFINED "USER DISPLAY SQ"
[The following figure is available in the .ps and .pdf version of
this document:]
Sample OLS Curves Generated for -.5 < x < 4.5
- -
Endnotes
[1] Supported on a PDP-10 System at MIT and available for the use at
UCSB by the way of APRA Network.
[2] [In this memo, the notation "(+)", "(-)", and "(*)" has been
substituted for a circle enclosing a +, -, and * symbol,
respectively.]
[This RFC was put into machine readable form for entry]
[into the online RFC archives by Helene Morin, Via Genie 12/1999]
