Ayad, Mohamed and Fleischmann, P. (2008) On the decomposition of rational functions. Journal of Symbolic Computation, 43 (4 ). 259-274 . ISSN 0747-7171.
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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.
|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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