منابع مشابه
Approximation of Continuous Functions by Means of Lacunary Polynomials
be the orthonormal trigonometric sums on Di for weight p(6)cr(0) ; if the u's and v's are uniformly bounded on a point set D2 contained in Di, the same is true of the U's and Vs. For this case the proof admits a materially simpler formulation than when geometric configurations are contemplated having the degree of generality previously considered. The details relating to the loci C', C", K, K',...
متن کاملOn 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 کاملAn Approximation by Lacunary Sequence of Vectors
Let (tk)k=0 be a sequence of real numbers satisfying t0 6= 0 and |tk+1| > (1+ 1/M)|tk| for each k > 0, where M > 1 is a fixed number. We prove that for any sequence of real numbers (ξk)k=0 there is a real number ξ such that ||tkξ−ξk|| > 1/(80M log(28M)) for each k > 0. Here, ||x|| denotes the distance from x ∈ R to the nearest integer. This is a corollary derived from our main theorem which is ...
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: Indagationes Mathematicae (Proceedings)
سال: 1977
ISSN: 1385-7258
DOI: 10.1016/1385-7258(77)90066-x