Homotopy techniques for multiplication modulo triangular sets

Authors:
Alin Bostan;Muhammad F. I. Chowdhury;Joris van der Hoeven;Éric Schost
Affiliations:
Algorithms Project, INRIA Rocquencourt, 78153 Le Chesnay Cedex, France;Computer Science Department, The University of Western Ontario, London, Ontario, Canada;CNRS, Département de Mathématiques, Université Paris-Sud, 91405 Orsay Cedex, France;Computer Science Department, The University of Western Ontario, London, Ontario, Canada
Venue:
Journal of Symbolic Computation
Year:
2011

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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.