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Practical divideandconquer algorithms for polynomial arithmetic
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Hart, William B. and Novocin, Andrew (2011) Practical divideandconquer algorithms for polynomial arithmetic. In: CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing, Kassel, Germany, 59 Sep 2011. Published in: Lecture Notes in Computer Science, Vol.6885 pp. 200214.

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Official URL: http://dx.doi.org/10.1007/9783642235689_16
Abstract
We investigate two practical divideandconquer 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:  03029743 
Official Date:  2011 
Volume:  Vol.6885 
Page Range:  pp. 200214 
Identification Number:  10.1007/9783642235689_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:  59 Sep 2011 
References:  1. D. Bernstein, Multiprecision Multiplication for Mathematicians, accepted by Advances in Applied Mathematics 
URI:  http://wrap.warwick.ac.uk/id/eprint/43601 
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