Parallel computation of resolvents by multimodular techniques and decomposition formula

Philippe Aubry 1 Annick Valibouze 2, 1, *
* Auteur correspondant
1 APR - Algorithmes, Programmes et Résolution
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : In this paper we significantly extend the limits of existing algebraic algorithms for computing Lagrange resolvents. Such algorithms are fundamental in effective Galois theory. However, they usually are of high complexity. For the case of absolute resolvents, N. Rennert has shown the value of a multimodular approach to reduce the complexity in space and time. We improve and generalize his work to the computation of any resolvent. In addition, we introduce a decomposition formula which allows us to split modular resolvents into resolvents of smaller degrees, thus both speeding computations and making it possible to efficiently parallelize them.
Type de document :
Article dans une revue
International Journal of Algebra and Computation, World Scientific Publishing, 2012, 22 (5), pp.1-21. 〈10.1142/S0218196712500439〉
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https://hal.archives-ouvertes.fr/hal-00694906
Contributeur : Annick Valibouze <>
Soumis le : lundi 7 mai 2012 - 09:47:55
Dernière modification le : jeudi 22 novembre 2018 - 14:36:46

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Philippe Aubry, Annick Valibouze. Parallel computation of resolvents by multimodular techniques and decomposition formula. International Journal of Algebra and Computation, World Scientific Publishing, 2012, 22 (5), pp.1-21. 〈10.1142/S0218196712500439〉. 〈hal-00694906〉

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