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. 2001.

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  • 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

  • cyclotomic — adjective a) of, or relating to cyclotomy b) of, or relating to the complex roots of unity <! this needs to be expanded …   Wiktionary

  • cyclotomic — cy·clo·tom·ic …   English syllables

  • 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 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 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 character — In number theory, a cyclotomic character is a character of a Galois group giving the Galois action on a group of roots of unity. As a one dimensional representation over a ring R, its representation space is generally denoted by R(1) (that is, it …   Wikipedia

  • Cyclotomic unit — In mathematics, a cyclotomic unit is a unit of an algebraic number field of the form (ζn − 1)/(ζ − 1) for ζ a root of unity, or more generally a unit that can be written as a product of these and a root of unity. The… …   Wikipedia

  • Cyclotomic identity — In mathematics, the cyclotomic identity states that where M is Moreau s necklace counting function, and μ(·) is the classic Möbius function of number theory. The name comes from the denominator, 1 − z j, which is the product of… …   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

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