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A Rational Function Decomposition Algorithm by Near-separated Polynomials

โœ Scribed by Cesar Alonso; Jaime Gutierrez; Tomas Recio

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
585 KB
Volume
19
Category
Article
ISSN
0747-7171

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โœฆ Synopsis

In this paper we present an algorithm for decomposing rational functions over an arbitrary coefficient field. The algorithm requires exponential time, but is more efficient in practice than the previous ones, including the polynomial time algorithm. Moreover, our algorithm is easier to implement. We also present some applications of rational function decomposition: (1) faithful re-parameterizing unfaithfully parameterized curves, (2) computing intermediate fields in a simple purely transcendental field extension (\mathbf{K}), and (3) providing a birationality test for subfields of (\mathbf{K}(x)). Several examples are computed using an implementation of our algorithm using MAPLE V.

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In this paper, we describe the application of a new version of Barnett's method to the squarefree decomposition of a univariate polynomial with coefficients in K[x], x being a parameter and K a characteristic zero field. This new version of Barnett's method uses Bezoutian matrices instead of matrice