- cyclotomic polynomial
- многочлен деления круга
English-Russian dictionary of technical terms. 2014.
cyclotomic polynomial
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Cyclotomic polynomial — In algebra, the nth cyclotomic polynomial, for any positive integer n, is the monic polynomial: where the product is over all nth primitive roots of unity ω in a field, i.e. all the complex numbers ω of order n. Contents 1 Properties … Wikipedia
Cyclotomic field — In number theory, a cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to Q, the field of rational numbers. The n th cyclotomic field Q(ζn) (with n > 2) is obtained by adjoining a primitive n… … Wikipedia
cyclotomic — I. | ̷ ̷ ̷ ̷ at cyclo +|tämik adjective : of or relating to cyclotomy II. adjective : relating to, being, or containing a polynomial of the form xp 1 + x … Useful english dictionary
cyclotomic — adjective Etymology: cyclotomy mathematical theory of the division of the circle into equal parts, from cycl + tomy Date: 1879 relating to, being, or containing a polynomial of the form xp 1 + xp 2 +…+ x + 1 where p is a prime number … New Collegiate Dictionary
cyclotomic — /suy kleuh tom ik, sik leuh /, adj. 1. of or pertaining to cyclotomy. 2. Math. (of a polynomial) irreducible and of the form xp 1 + xp 2 ± ... ± 1, where p is a prime number. [1875 80; CYCLOTOM(Y) + IC] * * * … Universalium
Reciprocal polynomial — In mathematics, for a polynomial p with complex coefficients,:p(z) = a 0 + a 1z + a 2z^2 + ldots + a nz^n ,!we define the reciprocal polynomial, p*:p^*(z) = overline{a} n + overline{a} {n 1}z + ldots + overline{a} 0z^n = z^noverline{p(ar{z}^{… … Wikipedia
All one polynomial — An all one polynomial (AOP) is a polynomial used in finite fields, specifically GF(2) (binary). The AOP is a 1 equally spaced polynomial.An AOP of degree m has all terms from x m to x 0 with coefficients of 1, and can be written as:AOP(x) = sum… … Wikipedia
Necklace polynomial — In combinatorial mathematics, the necklace polynomials, or (Moreau s) necklace counting function are the polynomials M(α,n) in α such that By Möbius inversion they are given by where μ is the classic Möbius function. The necklace polynomials are… … Wikipedia
Root of unity — The 5th roots of unity in the complex plane In mathematics, a root of unity, or de Moivre number, is any complex number that equals 1 when raised to some integer power n. Roots of unity are used in many branches of mathematics, and are especially … Wikipedia
Eisenstein's criterion — In mathematics, Eisenstein s criterion gives sufficient conditions for a polynomial to be irreducible over the rational numbers (or equivalently, over the integers; see Gauss s lemma). Suppose we have the following polynomial with integer… … Wikipedia
Proofs of quadratic reciprocity — In the mathematical field of number theory, the law of quadratic reciprocity, like the Pythagorean theorem, has lent itself to an unusual number of proofs. Several hundred proofs of the law of quadratic reciprocity have been found.Proofs that are … Wikipedia
