Determining Empirical Characteristics of Mathematical Expression Use

  • Clare M. So
  • Stephen M. Watt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3863)


Many processes in mathematical computing try to use knowledge of the most desired forms of mathematical expressions. This occurs, for example, in symbolic computation systems, when expressions are simplified, or mathematical document recognition, when formula layout is analyzed. The decision about which forms are the most desired, however, has typically been left to the guess-work or prejudices of a small number of system designers.

This paper observes that, on a domain by domain basis, certain expressions are actually used much more frequently than others. On the hypothesis that actual usage is the best measure of desirability, this papers begins to quantify empirically the use of common expressions in the mathematical literature. We analyze all 20,000 mathematical documents from the mathematical arXiv server from 2000-2004, the period corresponding to the new mathematical subject classification. We report on the process by which these documents are analyzed, through conversion to MathML, and present first empirical results on the most common aspects of mathematical expressions by subject classification. We use the notion of a weighted dictionary to record the relative frequency of subexpressions, and explore how this information may be used for further processes, including deriving common patterns of expressions and probability measures for symbol sequences.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Carlisle, D., Ion, P., Miner, R., Poppelier, N. (eds.): Mathematical Markup Language (MathML) Version 2.0 (2nd Edn.) W3C Recommendation. October 21 (2003),
  2. 2.
    ArXiv e-Print Archive,
  3. 3.
    Mathematical Subject Classification (2000), American Mathematical Society,
  4. 4.
  5. 5.
    Ontario Research Centre for Computer Algebra. On-line TeX to MathML translator (2002),
  6. 6.
    Plotkin, G.D.: A Note on Inductive Generalization. Machine Intelligence 5, 153–163 (1970)MathSciNetGoogle Scholar
  7. 7.
    So, C.M.: An Analysis of Mathematical Expressions Used in Practice. MSc. Thesis. University of Western Ontario (2005)Google Scholar
  8. 8.
    Stephen, M.: Watt. Implicit Mathematical Semantics in Conversion between TeX and MathML, TUGBoat 23(1) (2002)Google Scholar
  9. 9.
    Oancea, C., So, C., Watt, S.M.: Generalization in Maple. In: Maple Conference 2005, Maplesoft, pp. 377–382.Google Scholar
  10. 10.
    TeX4ht: LaTeX and TeX for Hypertext,

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Clare M. So
    • 1
  • Stephen M. Watt
    • 1
  1. 1.Ontario Research Centre for Computer Algebra, Department of Computer ScienceUniversity of Western OntarioLondonCanada

Personalised recommendations