Algebraic Numbers Satisfying Polynomials with Positive Rational Coefficients
نویسندگان
چکیده
منابع مشابه
Minimal Polynomials of Algebraic Numbers with Rational Parameters
It is unusual for an irreducible polynomial to have a root with rational real part or with rational imaginary part. Of course, such polynomials exist: one can simply take the minimal polynomial of, say, 1+ i √ 2 or √ 2+ i. The same applies to polynomials having a root of rational modulus. But it turns out to be of interest to characterize these three kinds of polynomials. We therefore define ou...
متن کاملFactoring Polynomials with Rational Coefficients
In this paper we present a polynomial-time algorithm to solve the following problem: given a non-zero polynomial f e Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive polynomials feZ[X] into irreducible factors in Z[X]. Here we call f ~ Z[X] primitive if the greatest comm...
متن کاملOn Algebraic Polynomials with Random Coefficients
The expected number of real zeros and maxima of the curve representing algebraic polynomial of the form a0 (n−1 0 )1/2 + a1 (n−1 1 )1/2 x + a2 (n−1 2 )1/2 x2 + · · · + an−1 (n−1 n−1 )1/2 xn−1 where aj , j = 0, 1, 2, . . . , n − 1, are independent standard normal random variables, are known. In this paper we provide the asymptotic value for the expected number of maxima which occur below a given...
متن کاملRoots of polynomials with positive coefficients
We describe the limit zero distributions of sequences of polynomials with positive coefficients. We also characterize the polynomials with real coefficients for which some power has positive coefficients. MSC Primary: 30C15, 26C10, secondary: 31A05.
متن کاملAn Inequality for Polynomials with Positive Coefficients and Applications in Rational Approximation
We extend an inequality of Leviatan and Lubinsky ([3: Theorem 3.1]) to polynomials with positive coefficients. Two applications in approximation by rational functions with prescribed numerators are given.
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: Journal of Numbers
سال: 2014
ISSN: 2356-7511,2314-842X
DOI: 10.1155/2014/296828