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Advanced Problem Solving

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axịom™

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Abstract

In this chapter we describe techniques useful in solving advanced problems with AXIOM.

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References

  1. For more information about the algebraic structure and properties of finite fields, see, for example, S. Lang, Algebra, Second Edition, New York: Addison-Wesley Publishing Company, Inc., 1984, ISBN 0 201 05487 6

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  2. R. Lidl, H. Niederreiter, Finite Fields, Encyclopedia of Mathematics and Its Applications, Vol. 20, Cambridge: Cambridge Univ. Press, 1983, ISBN 0 521 30240 4.

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  3. For For more information on the implementation aspects of finite fields, see J. Grabmeier, A. Scheerhorn, Finite Fields in Axiom, Technical Report, IBM Heidelberg Scientific Center, 1992.

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  4. Cf. Lidl, R. & Niederreiter, H., Finite Fields, Encycl. of Math. 20, (Addison-Wesley, 1983), p.90, Th. 3.18.

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  5. The existence of such polynomials is proved in Lenstra, H. W. & Schoof, R. J., Primitive Normal Bases for Finite Fields, Math. Comp. 48, 1987, pp. 217–231.

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  6. See McKay, Soicher, Computing Galois Groups over the Rationals, Journal of Number Theory 20, 273–281 (1983). We do not assume the results of this paper, however, and we continue with the computation.

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  7. The interested reader can learn more about these aspects of the AXIOM library from the paper “Computations in Algebras of Finite Rank,” by Johannes Grabmeier and Robert Wisbauer, Technical Report, IBM Heidelberg Scientific Center, 1992.

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  8. Worz-Busekros, A., Algebras in Genetics, Springer Lectures Notes in Biomathematics 36, Berlin e.a. (1980). In particular, see example 1.3.

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Authors and Affiliations

  1. IBM Thomas J. Watson Research Center, Route 134/Taconic Parkway, P.O. Box 218, 10598, Yorktown Heights, NY, USA

    Richard D. Jenks & Robert S. Sutor

Authors
  1. Richard D. Jenks
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  2. Robert S. Sutor
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© 1992 Springer Science+Business Media New York

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Jenks, R.D., Sutor, R.S. (1992). Advanced Problem Solving. In: axịom™. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2940-7_10

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  • DOI: https://doi.org/10.1007/978-1-4612-2940-7_10

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7729-3

  • Online ISBN: 978-1-4612-2940-7

  • eBook Packages: Springer Book Archive

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