Computer input/output of mathematical expressions

ABSTRACT

Studying mathematics is, in part, a language problem. Naturally, mathematicians are more likely to resist using a computer as a tool in their work if the tedious task of learning a new language for mathematics is part of the bargain. Furthermore, until a new language is thoroughly learned, difficulty in communication will make it less likely that their new experience will be a successful one. Beyond that, if a new computer language does not provide the same visual clues as standard mathematical notation, it may never adequately serve the mathematician. It therefore seems fair to assume that the computer input/output of mathematical expressions in a form resembling standard notation is an important goal. This form of expression is considerably more complex and expensive to handle than those used in, for example, the programming language FORTRAN. But the alternative (e.g., correctly manipulating a one page FORTRAN expression) is often quite painful.

REFERENCES

• 1: American Mathematical Society, Development of computer aids for tape-control of photo-composing machines, (Aug. 1968).
• 2: Anderson, R.H., Syntax-directed recognition of hand-printed two-dimensional mathematics, ACM Symposium on Interactive Systems for Experimental Applied Mathematics, Aug. 1967, Academic Press, New York, 1968.
• 3: Bernstein, M.I. and Williams, T.G., A two-dimensional programming system, Proc. IFIP Congress, 1968, (Aug. 1968).
• 4: Bernstein, M.I. and Howell, H.L., Hand-printed input for on-line systems: final report for phase I, Systems Development Corp. Report TM-(L)-39641000100,(April 14, 1968).
• 5: Frederick W. Blackwell , Robert H. Anderson, An on-line symbolic mathematics system using hand-printed two-dimensional notation, Proceedings of the 1969 24th national conference, p.551-557, August 26-28, 1969 [doi>10.1145/800195.805960]
• 6: Chang, Shi-kuo, A method for the structural analysis of two-dimensional mathematical expressions, IBM report RC 2654, (Oct.8, 1969).
• 7: Garber, H.N., A class of queueing problems, M.I.T. EE. PhD. Thesis 1956.
• 8: Griesmer, J. and Martin, W.A., Automatically breaking mathematical expressions into several lines, IBM Technical Disclosure Bulletin vol.10, no.6, (Nov. 1967).
• 9: Klerer, M. and Grossman, F., Further advances in two-dimensional input-output by typewriter terminals, Proc. FJCC 1967.
• 10: Klerer, M., Unpublished flowcharts at Hudson Laboratories, Columbia University, 1965.
• 11: Martin, W.A., Symbolic mathematical laboratory, M.I.T. Project MAC, MAC-TR-36, (Jan. 1967).
• 12: Millen, J.K., CHARYBDIS: A LISP program to display mathematical expressions on typewriter like devices, Symposium on Interactive Systems for Experimental Applied Mathematics, Aug.1967, Academic Press, New York, 1968.
• 13: Williams, T.G., On-line parsing of hand-printed mathematical expressions: final report for phase II, Systems Development Corp., Report NASA CR-1455.

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.1 Expressions and Their Representation

Additional Classification:
  B. Hardware
  B.4 INPUT/OUTPUT AND DATA COMMUNICATIONS
      B.4.2 Input/Output Devices

  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.1 Formal Definitions and Theory

  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.1 Hardware architecture
      I.3.3 Picture/Image Generation

General Terms:
Algorithms, Design, Performance, Theory