p551-blackwell - A N O N - L I N E SYMBOLIC MATHEMATICS...

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ANON-LINE SYMBOLIC MATHEMATICS SYSTEM USING HAND-PRINTED TWO-DIMENSIONAL 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 on-line manipulation of symbolic mathematical expressions. The primary input consists of the user's expressions hand-printed on a RAND tablet in ordinary two-dimensional 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 two-dimensional 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 non-programmer 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 two-di- 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 on-line environment)for explicit two-dimensional representations in communicating with the computer. 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 two-dimensional mathematical no- tation. The person at the console directs the transformations upon his expressions. Thus the system provides a kind of "so- phisticated scratchpad" for the user. System Design The goals of the system are several. First, it is hoped that it will be a use- ful mathematical tool for RAND scientists.
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This note was uploaded on 06/12/2011 for the course CAP 6105 taught by Professor Lavoila during the Spring '09 term at University of Central Florida.

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p551-blackwell - A N O N - L I N E SYMBOLIC MATHEMATICS...

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