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Article Dans Une Revue Foundations of Computational Mathematics Année : 2019

Effective power series computations

Résumé

Let K be an effective field of characteristic zero. An effective tribe is a subset of K[[z_1, z_2, ...]]=K ∪ K[[z_1]] ∪ K[[z_1, z_2]] ∪ ⋯ which is effectively stable under the K-algebra operations, restricted division, composition, the implicit function theorem, as well as restricted monomial transformations with arbitrary rational exponents. Given an effective tribe with an effective zero test, we will prove that an effective version of the Weierstrass division theorem holds inside the tribe, and that this can be used for the computation of standard bases
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Dates et versions

hal-00979357 , version 1 (15-04-2014)
hal-00979357 , version 2 (27-11-2016)

Identifiants

Citer

Joris van der Hoeven. Effective power series computations. Foundations of Computational Mathematics, 2019, 19 (3), pp.623-651. ⟨10.1007/s10208-018-9391-2⟩. ⟨hal-00979357v2⟩
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