**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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