منابع مشابه
On testing the divisibility of lacunary polynomials by cyclotomic polynomials
An algorithm is described that determines whether a given polynomial with integer coefficients has a cyclotomic factor. The algorithm is intended to be used for sparse polynomials given as a sequence of coefficientexponent pairs. A running analysis shows that, for a fixed number of nonzero terms, the algorithm runs in polynomial time.
متن کاملOn Generalized Difference Lacunary Statistical Convergence
A lacunary sequence is an increasing integer sequence θ = (kr) such that k0 =0, kr−kr−1 →∞ as r →∞. A sequence x is called Sθ(∆)− convergent to L provided that for each ε > 0, limr(kr − kr−1) {the number of kr−1 < k ≤ kr : |∆xk−L| ≥ ε} = 0, where ∆xk = ∆xk− ∆xk+1. The purpose of this paper is to introduce the concept of ∆ − lacunary statistical convergence and ∆-lacunary strongly convergence an...
متن کاملLacunary Statistical Convergence on Probabilistic Normed Spaces
In this paper, we study the concepts of lacunary statistical convergent and lacunary statistical Cauchy sequences in probabilistic normed spaces and prove some basic properties.
متن کاملFactoring bivariate sparse (lacunary) polynomials
We present a deterministic algorithm for computing all irreducible factors of degree ≤ d of a given bivariate polynomial f ∈ K[x, y] over an algebraic number field K and their multiplicities, whose running time is polynomial in the bit length of the sparse encoding of the input and in d . Moreover, we show that the factors over Q of degree ≤ d which are not binomials can also be computed in tim...
متن کاملDivisibility Test for Lacunary Polynomials
Given two lacunary (i.e. sparsely-represented) polynomials with integer coefficients, we consider the decision problem of determining whether one polynomial divides the other. In the manner of Plaisted [6], we call this problem 2SparsePolyDivis. More than twenty years ago, Plaisted identified as an open problem the question of whether 2SparsePolyDivis is in P [7]. Some progress has been made si...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1988
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-89-1-75-78