Abstract
This paper describes the algorithms used in an implementation of rational function integration in SAC-2, and gives a complexity analysis. The routines compute the transcendental part of the integral, expressing it over the extension field of least possible degree.
This was supported by a grant from the Deutscher Akademischer Austauschdienst.
Preview
Unable to display preview. Download preview PDF.
References
G E Collins, The Calculation of Multivariate Polynomial Resultants, Journal of the Association for Computing Machinery 18 No. 4(October 1971).
C Hermite, Oeuvres de Charles Hermite. 1912.
L Kronecker, Grundzüge einer arithmetischen Theorie der algebraischen Grössen, Journal für reine und angewante Mathematik 92(1882).
A Schönhage, Factorization of Univariate Integer Polynomials by Diophantine Approximation and an Improved Basis Reduction Algorithm, Lecture Notes in Computer Science 172(July 1984).
T J Smedley, Bounds for Algorithms on Polynomials Over Algebraic Extension Fields, Internal Report, University of Waterloo, (To Appear).
B M Trager, Algebraic Factoring and Rational Function Integration, Proc. ACM Symp. on Symbolic and Algebraic Computation, (1976).
P Weigel, Factorisierung von Polynomen über Q(α) nach einem verbesserten Algorithmus von Kronecker, Report No. 23/83, Universität Karlsruhe, (1983).
D Y Y Yun, Fast Algorithms for Rational Function Integration, Information Processing 77, North Holland Pub., (1977).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Smedley, T.J. (1986). Integration of rational functions in SAC-2. In: Calmet, J. (eds) Algebraic Algorithms and Error-Correcting Codes. AAECC 1985. Lecture Notes in Computer Science, vol 229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16776-5_742
Download citation
DOI: https://doi.org/10.1007/3-540-16776-5_742
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16776-1
Online ISBN: 978-3-540-39855-4
eBook Packages: Springer Book Archive