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The Algorithmization of Physics: Math Between Science and Engineering

  • Markus Rosenkranz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3249)

Abstract

I give a concise description of my personal view on symbolic computation, its place within mathematics and its relation to algebra. This view is exemplified by a recent result from my own research: a new symbolic solution method for linear two-point boundary value problems. The essential features of this method are discussed with regard to a potentially novel line of research in symbolic computation.

Keywords

Algebraic Structure Computer Algebra Symbolic Computation Congruence Class Single Layer Potential 
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.

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References

  1. 1.
    Buchberger, B.: An Algorithm for Finding a Basis for the Residual Class Ring of Zero-Dimensional Polynomial Ideal (in German). PhD Thesis, University of Innsbruck, Institute for Mathematics (1965) Google Scholar
  2. 2.
    Buchberger, B.: An Algorithmic Criterion for the Solvability of Algebraic Systems of Equations (in German). Æquationes Mathematicae 4, 374–383 (1970); In: [8], pp. 535– 545zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Buchberger, B.: Editorial. Journal of Symbolic Computation 1/1 (1985)Google Scholar
  4. 4.
    Buchberger, B.: Logic for Computer Science. Lecture Notes, Johannes Kepler University, Linz, Austria (1991)Google Scholar
  5. 5.
    Buchberger, B.: Symbolic Computation (in German). In: Pomberger, G., Rechenberg, P. (eds.) Handbuch der Informatik, pp. 955–974. Birkhäuser, München (1997)Google Scholar
  6. 6.
    Buchberger, B.: Introduction to Gröbner Bases. In: [8], pp. 3–31Google Scholar
  7. 7.
    Buchberger, B.: Loos, Rüdiger: Computer Algebra – Symbolic and Algebraic Computation. In: Buchberger, B., Collins, G.E., Loos, R. (eds.) Algebraic Simplification, Springer, Wien (1982)Google Scholar
  8. 8.
    Buchberger, B., Winkler, F.: Gröbner Bases and Applications. London Mathematical Society Lecture Notes, vol. 251. Cambridge University Press, Cambridge (1998)zbMATHGoogle Scholar
  9. 9.
    Corry, L.: Modern Algebra and the Rise of Mathematical Structures. Birkhäuser, Basel (1996)zbMATHGoogle Scholar
  10. 10.
    Courant, R., Hilbert, D.: Die Methoden der mathematischen Physik, vol. 1 & 2. Springer, Berlin (1993)Google Scholar
  11. 11.
    Kamke, E.: Differentialgleichungen und Lösungsmethoden (Volume 1), 10th edn. Teubner, Stuttgart (1983)Google Scholar
  12. 12.
    Lang, S.: Algebra. Springer, New York (2002)zbMATHGoogle Scholar
  13. 13.
    Lausch, H., Nöbauer, W.: Algebra of Polynomials. North-Holland, Amsterdam (1973)zbMATHGoogle Scholar
  14. 14.
    Rosenkranz, M.: The Green’s Algebra – A Polynomial Approach to Boundary Value Problems. PhD Thesis, Johannes Kepler University, Linz, Austria (2003)Google Scholar
  15. 15.
    Rosenkranz, M.: A New Symbolic Method for Solving Linear Two-Point Boundary Value Problems on the Level of Operators. Journal of Symbolic Computation (2004) (submitted); Also available as SFB Report 2003-41, Johannes Kepler University, Linz, Austria (2003)Google Scholar
  16. 16.
    Rosenkranz, M., Buchberger, B., Engl, H.W.: Solving Linear Boundary Value Problems via Non-commutative Gröbner Bases. Applicable Analysis 82/7, 655–675 (2003)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Rosenkranz, R., Buchberger, B., Engl, H.W.: Computer Algebra for Pure and Applied Functional Analysis. An FWF Proposal for F1322 Subproject of the SFB F013, Johannes Kepler University, Linz, Austria (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Markus Rosenkranz
    • 1
  1. 1.Johann Radon Institute for Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria

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