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Journal Articles Journal of Symbolic Computation Year : 2011

Homotopy techniques for multiplication modulo triangular sets

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Abstract

We study the cost of multiplication modulo triangular families of polynomials. Following previous work by Li et al. (2007), we propose an algorithm that relies on homotopy and fast evaluation-interpolation techniques. We obtain a quasi-linear time complexity for substantial families of examples, for which no such result was known before. Applications are given notably to additions of algebraic numbers in small characteristic.
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Dates and versions

hal-00819155 , version 1 (30-04-2013)

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Alin Bostan, Muhammad F. I. Chowdhury, Joris van Der Hoeven, Éric Schost. Homotopy techniques for multiplication modulo triangular sets. Journal of Symbolic Computation, 2011, 46 (12), pp.1378-1402. ⟨10.1016/j.jsc.2011.08.015⟩. ⟨hal-00819155⟩
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