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Practical divide-and-conquer algorithms for polynomial arithmetic

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Hart, William B. and Novocin, Andrew, 1983- (2011) Practical divide-and-conquer algorithms for polynomial arithmetic. In: CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing, Kassel, Germany, 5-9 Sep 2011. Published in: Lecture Notes in Computer Science, Vol.6885 pp. 200-214.

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Abstract

We investigate two practical divide-and-conquer style algorithms for univariate polynomial arithmetic. First we revisit an algorithm originally described by Brent and Kung for composition of power series, showing that it can be applied practically to composition of polynomials in Z[x] given in the standard monomial basis. We offer a complexity analysis, showing that it is asymptotically fast, avoiding coefficient explosion in Z[x]. Secondly we provide an improvement to Mulders' polynomial division algorithm. We show that it is particularly efficient compared with the multimodular algorithm. The algorithms are straightforward to implement and available in the open source FLINT C library. We offer a practical comparison of our implementations with various computer algebra systems.

Item Type: Conference Item (Paper)
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Algorithms, Computer science -- Mathematics
Journal or Publication Title: Lecture Notes in Computer Science
Publisher: Springer
ISSN: 0302-9743
Official Date: 2011
Volume: Vol.6885
Page Range: pp. 200-214
Identification Number: 10.1007/978-3-642-23568-9_16
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: Engineering and Physical Sciences Research Council (EPSRC) , France. Agence nationale de la recherche (ANR)
Grant number: EP/G004870/1 (EPSRC)
Conference Paper Type: Paper
Title of Event: CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
Type of Event: Conference
Location of Event: Kassel, Germany
Date(s) of Event: 5-9 Sep 2011
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URI: http://wrap.warwick.ac.uk/id/eprint/43601

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