ANONLINE SYMBOLIC MATHEMATICS SYSTEM
USING HANDPRINTED TWODIMENSIONAL NOTATION*
Frederick W. Blackwell
Robert H. Anderson
The RAND Corporation
Santa Monlca, Californla
Summary
This paper describes a system that is
being developed at The RAND Corporation
for the online manipulation of symbolic
mathematical expressions. The primary
input consists of the user's expressions
handprinted on a RAND tablet in ordinary
twodimensional mathematical notation.
The system recognizes the characters and
interprets the whole expression from the
spatial relationships present in ac
cordance with a previously input syntax.
The user at the console directs symbolic
transformations upon his input expressions
by instructing the computer to selectively
attempt to apply various rules of mathe
matics; these rules have been previously
entered into the system in the same manner
as the expressions. A transformed ex
pression resulting from the application
of a rule or group of rules is displayed
on the IBM 2250 graphic console. An ex
perimental version of the system is in
operation at the present time.
Introduction
Most programming languages employ
linear notation for algebraic formulas
not only because it is much easier to im
plement, but also because the relatively
few distinct types of twodimensional con
figurations which normally occur can be
readily represented in linear form. Fa
miliar examples are the use of the slash
for division and the use of the double
asterisk or some special character for ex
ponentlation. While the programmer and
nonprogrammer alike adapt to this linear
notation, we asst~ne that both would usu
ally prefer a language in which it is
possible to write in ordinary twodi
mensional mathematical notation. Examples
of how this can be done for typewriter
like devices are provided b X the work of
Klerer and May (1) and Wells (2), and for
more general input devices by the work of
Anderson (3) and Bernstein and Williams (4).
The latter systems are complicated by the
fact that the user prints his symbols on
a RAND tablet or similar device; the
characters must be individually recognized,
and then the whole formula must be properly
interpreted from the spatial relationships
present. The development of formula
manipulating languages, in which the data
and results are often inherently two
dimensional, has created additional demand
(intensified in an online environment)for
explicit twodimensional representations
in communicating with the computer.
This paper describes a system that is
being developed at The RAND Corporation
for the online manipulation of symbolic
mathematical expressions. The primary
input is the user's expressions hand
printed on a RAND tablet, and the primary
output consists of transformed expressions
which appear on the IBM 2250 graphical
display console. Both input and output
are in twodimensional mathematical no
tation. The person at the console directs
the transformations upon his expressions.
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 Spring '09
 LaVoila
 Expression, Donald Rumsfeld, Herman Kahn, Rule of inference

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