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Mathematics of Computation

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A recombination algorithm for the decomposition of multivariate rational functions

Author: Guillaume Chèze
Journal: Math. Comp. 82 (2013), 1793-1812
MSC (2010): Primary 11Y16, 68W30; Secondary 12Y05, 12D05, 13P05
Published electronically: November 30, 2012
MathSciNet review: 3042585
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Abstract: In this paper we show how we can compute in a deterministic way the decomposition of a multivariate rational function with a recombination strategy. The key point of our recombination strategy is the use of Darboux polynomials. We study the complexity of this strategy and we show that this method improves the previous ones. In the appendix, we explain how the strategy proposed recently by J. Berthomieu and G. Lecerf for the sparse factorization can be used in the decomposition setting. Then we deduce a decomposition algorithm in the sparse bivariate case and we give its complexity.

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Guillaume Chèze
Affiliation: Institut de Mathématiques de Toulouse, Université Paul Sabatier Toulouse 3, MIP Bât 1R3, 31 062 TOULOUSE cedex 9, France

Received by editor(s): November 3, 2010
Received by editor(s) in revised form: November 22, 2011
Published electronically: November 30, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.