Automatic Mathematical Translator /AMSTRAN/ permits scientists or engineers to enter mathematical equations in their natural mathematical format and to obtain an immediate graphical display of the solution. This automatic-programming, on-line, multiterminal computer system allows experienced programmers to solve nonroutine problems

Reinfelds, J.

Seitz, R. N.

Wood, L. H.

English

NASA Technical Reports Server

August 1966
	 Brief 66-10361 
NASA TECH BRIEF 
NASA Tech Briefs are issued to summarize specific innovations derived from the U. S. space 
program and to encourage their commercial application. Copies are available to the public from 
the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
New Computer System Simplifies Programming of Mathematical Equations 
The problem: 
To devise a low-cost desk-top computer system that 
will permit a scientist or engineer with no prior 
programming knowledge to solve problems in higher 
mathematics the way he now handles arithmetic prob-
lems on a desk-top calculator. The system should also 
provide the experienced programmer with the flexi-
bility he needs to solve nonroutine problems. 
The solution: 
An automatic-programming, on-line, multiterminal 
computer system, called AMTRAN (Automatic 
Mathematical Translator), which permits a scientist 
or engineer to enter mathematical equations in their 
natural mathematical format as they would appear in 
a textbook and to obtain an immediate graphical 
display of the solution on an oscilloscope. 
How it's done: 
The system consists of an operator keyboard, a 
storage and control keyboard, an oscilloscope, and an 
electric typewriter. Entry is made in two principal 
ways: through the keyboards, which provide several 
hundred of the more common functions and opera-
tions of mathematical analysis and through the type-
writer, which uses mnemonic labels to provide several 
thousand less common functions and operations. The 
system provides the user with graphical and alpha-
meric results as rapidly as the computer can obtain 
them. A rapid evaluation of intermediate results is 
afforded by the oscilloscope, with an attached Pola-
roid camera to provide a permanent record of the 
final results. 
As the equations are entered from the keyboard, the 
typewriter types out the equations in proper mathe-
matical format. At the end of each mathematical state-
ment, a carriage return button is depressed which
informs the computer that the mathematical statement 
has been completed and which causes a carriage return 
on the typewriter. When the carriage return button is 
depressed, a parenthesis count is made to ensure that 
parentheses have been properly closed. If such is not 
the case, the typewriter types out an abbreviated error 
message. If the user is unfamiliar with the system and 
wants to know what the abbreviated error message 
means, he may push an instructions button, where-
upon the typewriter types out the full error message. 
In this way, the experienced user does not have to wait 
for the type-out of the complete error message, while 
the beginner can call for it if he needs it. The instruc-
tions button also serves two other functions. At the 
beginning of operations, pressing the instructions 
button and then any other button provides a type-out 
giving the purpose of the other button and the rules 
for using it. The computer system also rejects im-
proper mathematical expressions. 
The user may operate in either a "desk calculator" 
mode or in a "stored program" mode. In the former, 
the computer executes operations as the user presses 
the buttons. At the same time, the computer tem-
porarily stores the list of button pushes made by the 
user. At the end of a mathematical statement, the user 
may transfer the entire statement to any one of a 
large number of unassigned blank buttons on the key-
board, making it part of the "stored program" mode. 
Thus, the user has the option of permanently retaining 
a pushbutton list of mathematical operations and 
transforming it into a portion of a stored program. 
The advantage of the desk calculator mode of opera-
tion is that the user can check the work at each step. 
For operations such as multiple integrations, which 
require an appreciable time to execute, the operator 
may elect to operate in the "stored program" mode. 
-	 (continued overleaf) 
This document was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States 
Government nor any person acting on behalf of the United States
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19660000360 2020-03-11T17:40:59+00:00Z
In this instance, a lighted execute button is pushed, 
causing the light to go out and suppressing execution. 
Then a list of button pushes (and mnemonic code 
type-ins) is entered without executing the associated 
opera(is When the carriage return button is- de- 
pressed at the end of the mathematical statement, the 
pushbutton list is terminated. The pushbutton list can 
then asigncd to a blank pushbutton or mnemonic 
call code as previously described, after which execu-
tion is restored. Complete programs are developed by 
embedding equations or sets of equations into a 
single pushbutton list. An entire program which may 
run for hours is then set into motion when a single 
button is pushed. 
The AMTRAN system. operates at three levels. 
First, it contains  real-time FORTRAN IV inter-
preter which permits the user to type in, execute, and 
debug FORTRAN programs on line. The user, if he 
wishes, may then automatically punch a FORTRAN 
source deck and process it in the conventional man-
ner. The second level provides tightly programmed 
operators for numerical analysis, and the third
level provides a large number of "convenience" op-
erators for classical analysis. The highest level at 
which the AMTRAN system may operate depends on 
the computer with which it is used. 
Notes:	 - 
I' The AMTRAN system lends itself exceedingly 
well to multistation, time-sharing operation. 
2. The system described was developed for use with 
the IBM 1620 and Univac 1107 computers, but is 
adaptable to other computer systems as well. 
3. Inquiries concerning this invention may be di-
rectedto: - 
Technology Utilization Officer 
Marshall Space Flight Center 
-	 Huntsville, Alabama 35812 
Reference: B66-10361 - 
Patent status: 
Inquiries about obtaining rights for the commercial 
use of this invention may be made to NASA, Code 
GP, Washington, D.C. 20546.
Source: Robert N. Seitz

Juris Reinfelds, and Lawrence H. Wood

(M-FS-441) 
B66-10361	 -	 Category 01


New computer system simplifies programming of mathematical equations

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