Homotopy techniques for multiplication modulo triangular sets

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

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