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EnglishIn 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 $Z[x]$. 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 (Shoup 2000). We give timings of this implementation on some difficult factorization problems.
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| Titolo: | Factorization in $Z[x]$: The Searching Phase | |
| Autori: | ||
| Data di pubblicazione: | 2000 | |
| 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 $Z[x]$. 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 (Shoup 2000). We give timings of this implementation on some difficult factorization problems. | |
| Handle: | http://hdl.handle.net/11567/509319 | |
| ISBN: | 1581132182 | |
| Appare nelle tipologie: | 04.01 - Contributo in atti di convegno |
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