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Communication Dans Un Congrès Année : 2009

High order derivatives and decomposition of multivariate polynomials

Jean-Charles Faugère
Ludovic Perret
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Résumé

In this paper, we present an improved method for decomposing multivariate polynomials. This problem, also known as the Functional Decomposition Problem (FDP) [17, 9, 27], is classical in computer algebra (e.g. [17, 18, 19, 23, 24, 7, 25]). Here, we propose to use high order partial derivatives to improve the algorithm described in [14]. Our new approach is more simple, and in some sense more natural. From a practical point of view, this new approach will lead to more efficient algorithms. The complexity of our algorithms will depend of the degree of the input polynomials, and the ratio n/u between the number of variables/polynomials.
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Dates et versions

hal-01294701 , version 1 (29-03-2016)

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Jean-Charles Faugère, Ludovic Perret. High order derivatives and decomposition of multivariate polynomials. ISSAC '09: the 2009 international symposium on Symbolic and algebraic computation, Jul 2009, Seoul, South Korea. pp.207-214, ⟨10.1145/1576702.1576732⟩. ⟨hal-01294701⟩
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