Advertisement

Rule-Based Simplification in Vector-Product Spaces

  • Songxin Liang
  • David J. Jeffrey
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4573)

Abstract

A vector-product space is a component-free representation of the common three-dimensional Cartesian vector space. The components of the vectors are invisible and formally inaccessible, although expressions for the components could be constructed. Expressions that have been built from the scalar and vector products can be simplified using a rule-based system. In order to develop and specify the system, an axiomatic system for a vector-product space is given. In addition, a brief description is given of an implementation in Aldor. The present work provides simplification functionality which overcomes difficulties encountered in earlier packages.

Keywords

Normal Form Transformation Rule Vector Product Vector Analysis Single Letter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aldor.org, Aldor User Guide (2002), http://www.aldor.org/docs/aldorug.pdf/
  2. 2.
    Belmonte, A., Yasskin, P.B.: A vector calculus package for Maple (2003), http://calclab.tamu.edu/maple/veccalc/
  3. 3.
    Chapman, S., Cowling, T.G.: The Mathematical Theory of Non-uniform Gases. Cambridge University Press, Cambridge (1939)Google Scholar
  4. 4.
    Cunningham, J.: Vectors. Heinemann Educational Books Ltd, London (1969)zbMATHGoogle Scholar
  5. 5.
    Eastwood, J.W.: OrthoVec: version 2 of the Reduce program for 3-d vector analysis in orthogonal curvilinear coordinates. Comput. Phys. Commun. 64, 121–122 (1991)CrossRefGoogle Scholar
  6. 6.
    Fiedler, B.: Vectan 1.1. Manual Math. Inst., Univ. Leipzig (1997)Google Scholar
  7. 7.
    Gibbs, J.W.: Elements of vector analysis. In: The Scientific Papers of J. Willard Gibbs, Dover (1961)Google Scholar
  8. 8.
    Harper, D.: Vector33: A Reduce program for vector algebra and calculus in orthogonal curvilinear coordinates. Comput. Phys. Commun. 54, 295–305 (1989)zbMATHCrossRefGoogle Scholar
  9. 9.
    Patterson, E.M.: Solving Problems in Vector Algebra. Oliver & Boyd Ltd, Edinburgh-London (1968)zbMATHGoogle Scholar
  10. 10.
    Qin, H., Tang, W.M., Rewoldt, G.: Symbolic vector analysis in plasma physics. Comput. Phys. Commun. 116, 107–120 (1999)zbMATHCrossRefGoogle Scholar
  11. 11.
    Silagadze, Z.K.: Multi-dimensional vector product. arXiv: math.ra, 0204357. (2002)Google Scholar
  12. 12.
    Stoutemyer, D.R.: Symbolic computer vector analysis. Computers & Mathematics with Applications 5, 1–9 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Tanimoto, S.L.: The Elements of Artificial Intelligence Using Common Lisp. Computer Science Press, New York (1990)Google Scholar
  14. 14.
    The Mathlab Group: Macsyma Reference Manual, vol. II, MIT, Cambridge (1983)Google Scholar
  15. 15.
    Wolfram, S.: The Mathematica Book. 3rd edn. Wolfram Media/Cambridge University Press (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Songxin Liang
    • 1
  • David J. Jeffrey
    • 1
  1. 1.Department of Applied Mathematics, University of Western Ontario, London, OntarioCanada

Personalised recommendations