On the decomposition of rational functions

Ayad, Mohamed and Fleischmann, P. (2008) On the decomposition of rational functions. Journal of Symbolic Computation, 43 (4 ). 259-274 . ISSN 0747-7171. (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.1016/j.jsc.2007.10.009

Abstract

Let f := p/q epsilon K(x) be a rational function in one variable. By Luroth's theorem, the collection of intermediate fields K(f) subset of L subset of K(x) is in bijection with inequivalent proper decompositions f = g circle h, with g, h epsilon K(x) of degrees >= 2. In [Alonso, Cesar, Gutierrez, Jaime, Recio, Tomas, 1995. A rational function decomposition algorithm by near-separated polynomials. J. Symbolic Comput. 19, 527-544] an algorithm is presented to calculate such a function decomposition. In this paper we describe a simplification of this algorithm, avoiding expensive solutions of linear equations. A MAGMA implementation shows the efficiency of our method. We also prove some indecomposability criteria for rational functions, which were motivated by computational experiments.

Item Type: Article
Uncontrolled keywords: rational function decomposition; indecomposable rational function; normal form of a rational function
Subjects: Q Science > QA Mathematics (inc Computing science) > QA 75 Electronic computers. Computer science
Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Peter Fleischmann
Date Deposited: 05 Feb 2009 13:43
Last Modified: 14 Jan 2010 14:33
Resource URI: http://kar.kent.ac.uk/id/eprint/8941 (The current URI for this page, for reference purposes)
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