Reduction of bivariate polynomials from convex-dense to dense, with application to factorizations
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- by Jérémy Berthomieu and Grégoire Lecerf PDF
- Math. Comp. 81 (2012), 1799-1821 Request permission
Abstract:
In this article we present a new algorithm for reducing the usual sparse bivariate factorization problems to the dense case. This reduction simply consists of computing an invertible monomial transformation that produces a polynomial with a dense size of the same order of magnitude as the size of the integral convex hull of the support of the input polynomial. This approach turns out to be very efficient in practice, as demonstrated with our implementation.References
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Additional Information
- Jérémy Berthomieu
- Affiliation: Laboratoire d’Informatique UMR 7161 CNRS, École polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France
- Address at time of publication: Laboratoire de Mathématiques UMR8100 CNRS, Université de Versailles-Sr-Quentin-en-Yvelynes, 45 avenue des États-Unis, 78035 Versailles Cedex, France
- Email: berthomieu@lix.polytechnique.fr
- Grégoire Lecerf
- Affiliation: Laboratoire d’Informatique UMR 7161 CNRS, École polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France
- Email: gregoire.lecerf@math.cnrs.fr
- Received by editor(s): October 15, 2010
- Received by editor(s) in revised form: March 28, 2011, and April 11, 2011
- Published electronically: November 10, 2011
- Additional Notes: This work was partly supported by the French ANR-09-JCJC-0098-01 MaGiX project, and by the Digiteo 2009-36HD grant of the Région Île-de-France.
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 81 (2012), 1799-1821
- MSC (2010): Primary ~12Y05; Secondary ~68W30, 11Y16, 12D05, 13P05
- DOI: https://doi.org/10.1090/S0025-5718-2011-02562-7
- MathSciNet review: 2904603