Computing in Transcendental Extensions

  • A. C. Norman
Part of the Computing Supplementa book series (COMPUTING, volume 4)


Performing the rational Operations in a field extended by a transcendental element is equivalent to performing arithmetic in the field of rational functions over the field. The computational difficulty associated with such extensions is in verifying that proposed extensions are transcendental. When the extensions being considered are functions, and where a differentiation operator can be defined for them, strueture theorems can be used to determine the character of the extension and to exhibit a relationship between the adjoined element and existing quantities in case the adjoined element is not transcendental.


Structure Theorem Transcendental Function Rational Operation Diophantine Approximation Constant Field 
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    Caviness, B. F.: Methods for Symbolic Computation with Transcendental Functions. MAXIMIN 1977, 16–43.Google Scholar
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    Kaplansky, I.: An Introduetion to Differential Algebra. Paris: Hermann 1957.Google Scholar
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    Lang, S.: Transcendental Numbers and Diophantine Approximations. Bull. AMS 77/5, 635–677.Google Scholar
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    Rothstein, M., Caviness, B. F.: A Strueture Theorem for Exponential and Primitive Functions. SIAM J. Computing 8/3, 357–367 (1979).CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag/Wien 1983

Authors and Affiliations

  • A. C. Norman
    • 1
  1. 1.Computer LaboratoryUniversity of CambridgeCambridgeUnited Kingdom

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