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The Eisenstein integers, sometimes also called the Eisenstein-Jacobi integers (Finch 2003, p. 601), are numbers of the form a+bomega, where a and b are normal integers, ...

The Eisenstein units are the Eisenstein integers +/-1, +/-omega, +/-omega^2, where omega = 1/2(-1+isqrt(3)) (1) omega^2 = 1/2(-1-isqrt(3)). (2)

Let omega be the cube root of unity (-1+isqrt(3))/2. Then the Eisenstein primes are Eisenstein integers, i.e., numbers of the form a+bomega for a and b integers, such that ...

One of the numbers ..., -2, -1, 0, 1, 2, .... The set of integers forms a ring that is denoted Z. A given integer n may be negative (n in Z^-), nonnegative (n in Z^*), zero ...

An Eisenstein series with half-period ratio tau and index r is defined by G_r(tau)=sum^'_(m=-infty)^inftysum^'_(n=-infty)^infty1/((m+ntau)^r), (1) where the sum sum^(') ...

Eisenstein's irreducibility criterion is a sufficient condition assuring that an integer polynomial p(x) is irreducible in the polynomial ring Q[x]. The polynomial ...

A synonym for integer. The word "rational" is sometimes used for emphasis to distinguish it from other types of "integers" such as cyclotomic integers, Eisenstein integers, ...

A Gaussian integer is a complex number a+bi where a and b are integers. The Gaussian integers are members of the imaginary quadratic field Q(sqrt(-1)) and form a ring often ...

The function intx gives the integer part of x. In many computer languages, the function is denoted int(x). It is related to the floor and ceiling functions |_x_| and [x] by ...

An integer that is either 0 or positive, i.e., a member of the set Z^*={0} union Z^+, where Z-+ denotes the positive integers.