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, Moreno Maza and Schost, 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 to notably addition of algebraic numbers in small characteristic.

Authors: Alin Bostan, Muhammad Chowdhury, Joris van der Hoeven, Éric Schost

Keywords: Triangular sets, multiplication, complexity

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