منابع مشابه
Aurifeuillian factorization
The Cunningham project seeks to factor numbers of the form bn±1 with b = 2, 3, . . . small. One of the most useful techniques is Aurifeuillian Factorization whereby such a number is partially factored by replacing bn by a polynomial in such a way that polynomial factorization is possible. For example, by substituting y = 2k into the polynomial factorization (2y2)2+1 = (2y2−2y+1)(2y2+2y+1) we ca...
متن کاملComputing Aurifeuillian Factors
For odd square-free n > 1, the cyclotomic polynomial Φn(x) satisfies an identity Φn(x) = Cn(x) ± nxDn(x) of Aurifeuille, Le Lasseur and Lucas. Here Cn(x) and Dn(x) are monic polynomials with integer coefficients. These coefficients can be computed by simple algorithms which require O(n2) arithmetic operations over the integers. Also, there are explicit formulas and generating functions for Cn(x...
متن کاملLempel-Ziv factorization: Simple, fast, practical
For decades the Lempel-Ziv (LZ77) factorization has been a cornerstone of data compression and string processing algorithms, and uses for it are still being uncovered. For example, LZ77 is central to several recent text indexing data structures designed to search highly repetitive collections. However, in many applications computation of the factorization remains a bottleneck in practice. In th...
متن کامل$n$-factorization Property of Bilinear Mappings
In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity...
متن کاملWZ factorization via Abay-Broyden-Spedicato algorithms
Classes of Abaffy-Broyden-Spedicato (ABS) methods have been introduced for solving linear systems of equations. The algorithms are powerful methods for developing matrix factorizations and many fundamental numerical linear algebra processes. Here, we show how to apply the ABS algorithms to devise algorithms to compute the WZ and ZW factorizations of a nonsingular matrix as well as...
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2008
ISSN: 1246-7405
DOI: 10.5802/jtnb.641