Irreducibility testing and factorization of polynomials
نویسندگان
چکیده
منابع مشابه
Prime Values of Polynomials and Irreducibility Testing
In 1857 Bouniakowsky [6] made a conjecture concerning prime values of polynomials that would, for instance, imply that x + 1 is prime for infinitely many integers x. Let ƒ (x) be a polynomial with integer coefficients and define the fixed divisor of ƒ, written d(ƒ), as the largest integer d such that d divides f(x) for all integers x. Bouniakowsky conjectured that if f(x) is nonconstant and irr...
متن کاملIrreducibility testing of lacunary 0, 1-polynomials
A reciprocal polynomial g(x) ∈ Z[x] is such that g(0) 6= 0 and if g(α) = 0 then g(1/α) = 0. The non-reciprocal part of a monic polynomial f(x) ∈ Z[x] is f(x) divided by the product of its irreducible monic reciprocal factors (to their multiplicity). This paper presents an algorithm for testing the irreducibility of the nonreciprocal part of a 0, 1-polynomial (a polynomial having each coefficien...
متن کاملDeterministic Irreducibility Testing of Polynomials over Large Finite Fields
We present a sequential deterministic polynomial-time algorithm for testing dense multivariate polynomials over a large finite field for irreducibility. All previously known algorithms were of a probabilistic nature. Our deterministic solution is based on our algorithm for absolute irreducibility testing combined with Berlekamp’s algorithm.
متن کاملIrreducibility of Hecke Polynomials
In this note, we show that if the characteristic polynomial of some Hecke operator Tn acting on the space of weight k cusp forms for the group SL2(Z ) is irreducible, then the same holds for Tp, where p runs through a density one set of primes. This proves that if Maeda’s conjecture is true for some Tn, then it is true for Tp for almost all primes p.
متن کاملFactors and Irreducibility of Generalized Stern Polynomials
We investigate an infinite class of polynomial sequences at(n; z) with integer parameter t 1, which reduce to the well-known Stern (diatomic) sequence when z = 1 and are (0, 1)-polynomials when t 2. These sequences are related to the theory of hyperbinary expansions. The main purpose of this paper is to obtain various irreducibility and factorization results, most of which involve cyclotomic po...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1983
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1983-0717715-6