@inproceedings{090d0bdedc1046b3b8cb329bdc296aa6,
title = "Composition modulo powers of polynomials",
abstract = "Modular composition is the problem to compose two univariate polynomials modulo a third one. For polynomials with coefficients in a finite field, Kedlaya and Umans proved in 2008 that the theoretical bit complexity for performing this task could be made arbitrarily close to linear. Unfortunately, beyond its major theoretical impact, this result has not led to practically faster implementations yet. In this paper, we study the more specific case of composition modulo the power of a polynomial. First we extend previously known algorithms for power series composition to this context.We next present a fast direct reduction of our problem to power series composition.",
keywords = "Algorithm, Complexity, Modular composition, Series composition",
author = "\{Van Der Hoeven\}, Joris and Gr{\'e}goire Lecerf",
note = "Publisher Copyright: {\textcopyright} 2017 Copyright held by the owner/author(s).; 42nd ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2017 ; Conference date: 25-07-2017 Through 28-07-2017",
year = "2017",
month = jul,
day = "23",
doi = "10.1145/3087604.3087634",
language = "English",
series = "Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC",
publisher = "Association for Computing Machinery",
pages = "445--452",
editor = "Michael Burr",
booktitle = "ISSAC 2017 - Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation",
}