Abstract
We describe an algorithm for computing symbolic limits, i.e. limits of expressions in symbolic form, using hierarchical series. A hierarchical series consists of two levels: an inner level which uses a simple generalization of Laurent series with finite principal part and which captures the behaviour of subexpressions without essential singularities, and an outer level which captures the essential singularities. Once such a series has been computed for an expression at a given point, the limit of the expression at the point is determined by looking at the most significant term of the series. By this method one can compute, for example, the limit of:
This algorithm solves the limit problem for a large class of expressions.
Extended Abstract
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Paul S. Wang, Automatic Computation of Limits, pp. 458–464 in Proceedings of the Second Symposium on Symbolic and Algebraic Manipulation, ed. S.R. Petrick, Special Interest Group on Symbolic and Algebraic Manipulation, Association for Computing Machinery (1971).
W.A. Martin and R.J. Fateman, The MACSYMA System, pp. 59–75 in Proceedings of the Second Symposium on Symbolic and Algebraic Manipulation, ed. S.R. Petrick, Special Interest Group on Symbolic and Algebraic Manipulation, Association for Computing Machinery (1971).
Bruce W. Char, Gregory J. Fee, Keith O. Geddes, Gaston H. Gonnet, and Michael B. Monagan, A tutorial introduction to Maple, Journal of Symbolic Computation 2(2) pp. 179–200 (1986).
R.H. Risch, The problem of integration in finite terms, Trans. Am. Math. Soc. 139 pp. 167–189 (1969).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Geddes, K.O., Gonnet, G.H. (1989). A new algorithm for computing symbolic limits using hierarchical series. In: Gianni, P. (eds) Symbolic and Algebraic Computation. ISSAC 1988. Lecture Notes in Computer Science, vol 358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51084-2_47
Download citation
DOI: https://doi.org/10.1007/3-540-51084-2_47
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51084-0
Online ISBN: 978-3-540-46153-1
eBook Packages: Springer Book Archive