Part of the Computing Supplementa book series (COMPUTING, volume 4)


In this introduction we first give a working defmition of Computer algebra. We then describe the Organization of research activities in this field. Finally the overall structure and the intention of the present volume on Computer algebra is explained. Some technical information (basic references, notation etc.) about the volume is given.


Computer Algebra Algebraic Manipulation Computer Algebra System Algebraic Computation Finite Precision 
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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  1. [1]
    Aho, A. U., Hopcroft, J. E., Ullman, J. D.: The Design and Analysis of Computer Algorithms. Reading, Mass.: Addison-Wesley 1974.MATHGoogle Scholar
  2. [2]
    Birkhoff, G.: The Role of Modern Algebra in Computing. SIAM Proc. 1971, 1–47.Google Scholar
  3. [3]
    Birkhoff, G.: Current Trends in Algebra. Am. Math. Mon. 80/7, 760–762 (1973).CrossRefMATHMathSciNetGoogle Scholar
  4. [4]
    Birkhoff, G., Lipson, J.: Heterogeneous Algebra. J. Comb. Theory 8, 115–133 (1970).CrossRefMATHMathSciNetGoogle Scholar
  5. [5]
    Borodin, A. B., Munro, I.: The Computational Complexity of Algebraic and Numerie Problems. New York: American Elsevier 1975.Google Scholar
  6. [6]
    Brainerd, W. S., Landweber, L. H.: Theory of Computation. New York: J. Wiley 1974.Google Scholar
  7. [7]
    Buchberger, B., Lichtenberger, F.: Mathematik für Informatiker I (Die Methoden der Mathematik), 2nd ed. Berlin-Heidelberg-New York: Springer 1981.CrossRefGoogle Scholar
  8. [8]
    Collins, G. E.: Computer Algebra of Polynomials and Rational Functions. Am. Math. Mon. 80/7, 725–755 (1973).CrossRefMATHGoogle Scholar
  9. [9]
    Griesmer, J. H.: The State of Symbolic Computation. SIGSAM Bull. 13/3, 25–28 (1979).CrossRefGoogle Scholar
  10. [10]
    Hasse, H.: Höhere Algebra I. Berlin: De Gruyter 1957.Google Scholar
  11. [11]
    Hermann, G.: Die Frage der endlich vielen Schritte in der Theorie der Polynomideale. Math. Ann. 95, 736–788 (1926).CrossRefMATHMathSciNetGoogle Scholar
  12. [12]
    Knuth, D. E.: The Art of Computer Programming, Vol. I-III. Reading, Mass.: 1968–1981.MATHGoogle Scholar
  13. [13]
    Knuth, D. E.: Algorithms. Scientific American 2364, 63–80 (1977).MathSciNetGoogle Scholar
  14. [14]
    Kronecker, L.: Werke (Hensel, K., ed.). Leipzig: 1845.Google Scholar
  15. [15]
    Lipson, J. D.: Algebra and Algebraic Computing. London: Addison-Wesley 1981.MATHGoogle Scholar
  16. [16]
    van der Waerden, B. L.: Modern Algebra, Vol. I and II. New York: Frederick Ungar 1953.Google Scholar
  17. [17]
    Weyl, H.: Randbemerkungen zu Hauptproblemen der Mathematik II: Fundamentalsatz der Algebra und Grundlagen der Mathematik. Math. Z. 20, 131–150 (1924).CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag/Wien 1983

Authors and Affiliations

  • R. Loos
    • 1
  1. 1.Institut für Informatik IUniversität Karlsruhe Zirkel 2KarlsruheFederal Republic of Germany

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