Skip to main content
Springer Nature Link
Log in

Processing Textbook-Style Matrices

  • Conference paper
Mathematical Knowledge Management (MKM 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3863))

Included in the following conference series:

Abstract

In mathematical textbooks matrices are often represented as objects of indefinite size containing abbreviations. To make the knowledge implicitly given in these representations available in electronic form they have to be interpreted correctly. We present an algorithm that provides the interface between the textbook style representation of matrix expressions and their concrete interpretation as formal mathematical objects. Given an underspecified matrix containing ellipses and fill symbols, our algorithm extracts the semantic information contained. Matrices are interpreted as a collection of regions that can be interpolated with a particular term structure. The effectiveness of our procedure is demonstrated with an implementation in the computer algebra system Maple.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Char, B.W., Geddes, K.O., Gonnet, G.H., Leong, B., Monagan, M.B., Watt, S.M.: Maple V: Language Reference Manual. Springer, Heidelberg (1991)

    Google Scholar 

  2. Fateman, R.: Manipulation of matrices symbolically (January 9 2003), Available from http://http.cs.berkeley.edu/~fateman/papers/symmat2.pdf

  3. Fitting, M.: First-Order Logic and Automated Theorem Proving. Springer, Heidelberg (1990)

    MATH  Google Scholar 

  4. Heck, A.: Maple Manuals, 3rd edn. Springer, Heidelberg (2003)

    Google Scholar 

  5. Horn, R., Johnson, C.: Matrix Analysis. Cambridge University Press, Cambridge (1990)

    MATH  Google Scholar 

  6. Kanahori, T., Suzuki, M.: A recognition method of matrices by using variable block pattern elements generating rectangular areas. In: Blostein, D., Kwon, Y.-B. (eds.) GREC 2001. LNCS, vol. 2390, p. 320. Springer, Heidelberg (2002)

    Google Scholar 

  7. Pollet, M., Sorge, V., Kerber, M.: Intuitive and formal representations: The case of matrices. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 317–331. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  8. Sexton, A., Sorge, V.: Semantic analysis of matrix structures. In: International Conference in Document Analysis and Recognition. IAPR (2005) (to appear)

    Google Scholar 

  9. Snyder, W.: A Proof Theory for General Unification, Birkhäuser. Progress in Computer Science and Applied Logic, vol. 11 (1991)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science, University of Birmingham, UK

    Alan Sexton & Volker Sorge

Authors
  1. Alan Sexton
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Volker Sorge
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Computer Science, Jacobs University Bremen,  

    Michael Kohlhase

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sexton, A., Sorge, V. (2006). Processing Textbook-Style Matrices. In: Kohlhase, M. (eds) Mathematical Knowledge Management. MKM 2005. Lecture Notes in Computer Science(), vol 3863. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11618027_8

Download citation

  • DOI: https://doi.org/10.1007/11618027_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31430-1

  • Online ISBN: 978-3-540-31431-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics