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+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"
+
+   MIT MATHLAB PDP-10
+
+   ML ITS.796. DDT.514.
+   9. USERS
+
+   :LOGIN WMP                              Login to MIT-MATHLAB.
+
+
+   :MACSYMA                                Call up MACSYMA
+
+   THIS IS MACSYMA 212
+
+   USE " INSTEAD OF ?
+   SEE UPDATE > MACSYM;
+
+   FIX 212 DSK MACSYM BEING LOADED
+   LOADING DONE
+
+   (C1) BATCH(BATCH,UTILS);                Load BATCH UTILS file.
+
+   (UREAD BATCH UTILS DSK WMP) FILE NOT FOUND
+
+   (C2) BATCH(BATCH,UTILS,DSK,UCSB);
+
+   (C2) LISTX:();
+   (D2)                                    ()
+
+   (C3) ADDLIST(X):=LISTX:CONS(X,LISTX);
+   (D3)                   ADDLIST(X) := (LISTX : CONS(X, LISTX))
+
+
+
+Parrish & Pickins                                               [Page 6]
+
+RFC 525                MIT-MATHLAB MEETS UCSB-OLS            1 June 1973
+
+
+   (C4) SAVE(FILENAME):=APPLY(STRINGOUT,APPEND(
+              CONS((FILENAME,BATCH,DSK,UCSB),REVERSE(LISTX)),("?")));
+   (D4) SAVE(FILENAME) :=
+        APPLY(STRINGOUT,APPEND(CONS((FILENAME, BATCH, DSK, UCSB),
+        REVERSE(LISTX)),(?)))
+
+   (D5)                                          BATCH DONE
+
+   (C6) (X**2+3)/(X+1);
+                                                2
+                                               X  + 3
+   (D6)                                        -------
+                                                X + 1
+   (C7) INTEGRATE(%,X);
+
+   SIN FASL DSK MACSYM BEING LOADED
+   LOADING DONE                                2
+                                              X  - 2 X
+   (D7)                                      ----------  + 4 LOG(X + 1)
+                                                2
+   (C8) ADDLIST('D6);
+   (D8)                                       (D6)
+
+   (C9) ADDLIST('D7);
+   (D9)                               (D7, D6)   Use ADDLIST function
+                                        to save line numbers D6 and D7.
+
+   (C10) DIFF(D6,X);
+                                              2
+                                     2 X     X  + 3
+   (D10)                            ----  -  ------
+                                     X+1          2
+                                             (X+1)
+
+   (C11) ADDLIST('D10);
+   (D11)                      (D10, D7, D6)   Use ADDLIST function to
+                                              save line number D10.
+
+   (C12) SAVE(MYFILE);
+   (D12)                     (D6, D7, D10, ?)  Write list of lines out
+                                                  to a disk file using
+   (C13) *********Z     Leave MACSYMA                   SAVE function.
+   25156)    .IOT 1,1
+
+   :LISTF UCSB
+
+
+   DSK UCSB
+
+
+
+Parrish & Pickins                                               [Page 7]
+
+RFC 525                MIT-MATHLAB MEETS UCSB-OLS            1 June 1973
+
+
+   FREE BLCCKS UO #1 241 U1 #3 345 U2 #5 379
+
+   3    ATTN     BATCH  1  5/23/73  13:53:11
+   1    BATCH    UTILS  1  5/23/73  13:11:43
+   3    DEMO     WMP    1  5/26/73  15:29:26
+   5    DEMO1    BATCH  1  4/29/73  22:41:17
+   1    DEMO99   BATCH  1  5/25/73  00:07:15
+   5    MYFILE   BATCH  1  5/31/73  12:41:50 <-- file is in directory
+   1    _MSGS_   UCSB   0  5/26/73  21:13:53     at MATHLAB
+
+   :LOGOUT
+                                               Logout and disconnect.
+   -------------------------------------------------------------------
+   ML ITS 796 CONSOLE 24 FREE. 12:42:35
+
+   DISCONNECTION COMPLETE
+   WORK AREAS UPDATED                         Load Retrieval program
+   LOAD MATHLAB                             "SYST LOAD MATHLAB RETURN"
+   FILE LOADED
+
+                                          "USER LO (+)"
+   RETRIEVE EXPRESSIONS
+   --------------------
+
+   MATHLAB FILE? (EXP)
+   -->MYFILE-->MYFILE.                    "MYFILE ENTER"
+   OLS FILE?  (MYFILE)
+   -->demo11-->demo11                     "demo11 ENTER"
+   OLS FILE
+   PROTECT CODE?  ()                      "demo11 ENTER"
+   -->DEMO-->demo11
+   BATCH JOBNAME? (MYFILE)                "PARSET ENTER"
+   -->PARSET-->PARSET.
+
+   PRESS ENTER TO SUBMIT JOB              "ENTER"
+
+   VOLUME NEEDED=
+   JOB SUBMITTED
+
+   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]
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Parrish & Pickins                                               [Page 9]
+