Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Caviness, B. F.: Methods for Symbolic Computation with Transcendental Functions. MAXIMIN 1977, 16–43.
Kaplansky, I.: An Introduetion to Differential Algebra. Paris: Hermann 1957.
Lang, S.: Transcendental Numbers and Diophantine Approximations. Bull. AMS 77/5, 635–677.
Rothstein, M., Caviness, B. F.: A Strueture Theorem for Exponential and Primitive Functions. SIAM J. Computing 8/3, 357–367 (1979).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer-Verlag/Wien
About this chapter
Cite this chapter
Norman, A.C. (1983). Computing in Transcendental Extensions. In: Buchberger, B., Collins, G.E., Loos, R., Albrecht, R. (eds) Computer Algebra. Computing Supplementa, vol 4. Springer, Vienna. https://doi.org/10.1007/978-3-7091-7551-4_11
Download citation
DOI: https://doi.org/10.1007/978-3-7091-7551-4_11
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-81776-6
Online ISBN: 978-3-7091-7551-4
eBook Packages: Springer Book Archive