- In mathematics, the nth
cyclotomic polynomial, for any
positive integer n, is the
unique irreducible polynomial with
integer coefficients that is a divisor...
- In
algebraic number theory, a
cyclotomic field is a
number field obtained by
adjoining a
complex root of
unity to Q {\displaystyle \mathbb {Q} } , the...
- In mathematics, the
cyclotomic identity states that 1 1 − α z = ∏ j = 1 ∞ ( 1 1 − z j ) M ( α , j ) {\displaystyle {1 \over 1-\alpha z}=\prod _{j=1}^{\infty...
- This
geometric fact
accounts for the term "
cyclotomic" in such
phrases as
cyclotomic field and
cyclotomic polynomial; it is from the Gr****
roots "cyclo"...
-
primality test (also
known as Agrawal–Kayal–Saxena
primality test and
cyclotomic AKS test) is a
deterministic primality-proving
algorithm created and published...
- Aurifeuille, is
factorization of
certain integer values of the
cyclotomic polynomials.
Because cyclotomic polynomials are
irreducible polynomials over the integers...
-
subfields Q {\displaystyle \mathbb {Q} } (cos(2π/2n)) of the 2-power
cyclotomic fields Q {\displaystyle \mathbb {Q} } (ζ2n) (where n is a
positive integer)...
- a field, or a
subextension of such an extension. The
cyclotomic fields are examples. A
cyclotomic extension,
under either definition, is
always abelian...
- 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...
- In mathematics, a
cyclotomic unit (or
circular unit) is a unit of an
algebraic number field which is the
product of
numbers of the form (ζa n − 1) for...
