Advertisement

Abstracting symbolic matrices

Special issue on artificial intelligence and symbolic computation
  • Randa Almomen
  • Alan P. Sexton
  • Volker SorgeEmail author
Article

Abstract

We present a procedure that allows the abstraction of elements in concrete symbolic matrices to obtain a more compact representation employing ellipses in order to expose homogeneous regions present in a matrix. We furthermore extend that procedure to allow for generalisations of concrete matrices to an abstract form that enables us to determine the generic type of a given matrix. The presented algorithms employ artificial intelligence techniques such as pattern recognition and constraint solving.

Keywords

Symbolic matrices Abstract matrices Ellipsis terms 

Mathematics Subject Classifications (2010)

68W30 15A99 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Almomen, R.: Abstracting symbolic matrices. Master’s thesis, School of Computer Science, University of Birmingham (2010)Google Scholar
  2. 2.
    Maplesoft: Maple User Manual. Maplesoft (2011)Google Scholar
  3. 3.
    Murdoch, D.J., Chow, E.D.: A graphical display of large correlation matrices. Amer. Statist. 50, 178–180 (1996)Google Scholar
  4. 4.
    Plotkin, G.D.: A note on inductive generalization. In: Proc. of the Fifth Annual Machine Intelligence Workshop, Machine Intelligence 5, pp. 153–163, Edinburgh University Press (1970)Google Scholar
  5. 5.
    Sexton, A.P., Sorge, V.: Abstract matrices in symbolic computation. In: Proceedings of ISSAC 2006, pp. 318–325. ACM Press (2006)Google Scholar
  6. 6.
    Sexton, A.P., Sorge, V., Watt, S.M.: Computing with abstract matrix structures. In: Proc. of ISSAC’2009, pp. 325–332. ACM Press (2009)Google Scholar
  7. 7.
    Sexton, A.P., Sorge, V., Watt, S.M.: Reasoning with generic cases in the arithmetic of abstract matrices. In: Proc. of Calculemus 2009. LNAI, vol. 5625, pp. 138–153. Springer (2009)Google Scholar
  8. 8.
    Wolfram Research, Inc.: Mathematica Edition: Version 8.0. Wolfram Research, Inc. (2010)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.School of Computer ScienceUniversity of BirminghamBirminghamUK

Personalised recommendations