# Factorization in Z[x]: the searching phase

1 POLKA - Polynomials, Combinatorics, Arithmetic
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : In this paper we describe ideas used to accelerate the Searching Phase of the Berlekamp--Zassenhaus algorithm, the algorithm most widely used for computing factorizations in $\ZZ[x]$. Our ideas do not alter the theoretical worst-case complexity, but they do have a significant effect in practice: especially in those cases where the cost of the Searching Phase completely dominates the rest of the algorithm. A complete implementation of the ideas in this paper is publicly available in the library NTL~\cite{Shoup00}. We give timings of this implementation on some difficult factorization problems.
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Conference papers
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https://hal.inria.fr/inria-00099116
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Submitted on : Tuesday, September 26, 2006 - 8:51:06 AM
Last modification on : Friday, February 26, 2021 - 3:28:02 PM

### Identifiers

• HAL Id : inria-00099116, version 1

### Citation

John Abbott, Victor Shoup, Paul Zimmermann. Factorization in Z[x]: the searching phase. International Symposium on Symbolic and Algebraic Computation - ISSAC 2000, Aug 2000, St Andrews/United Kingdom, pp.1--7. ⟨inria-00099116⟩

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