English Dictionary

Eisenstein integer

noun

(algebra) A complex number of the form a+b𝜔, where a and b are integers and ω is defined by the following two rules: (1) 𝜔³=1 and (2) 1+𝜔+𝜔²=0; an element of the Euclidean domain ℤ[𝜔].

An Eisenstein integer is a complex number of the form a+b𝜔.

意味（1）

(algebra) A complex number of the form a+b𝜔, where a and b are integers and ω is defined by the following two rules: (1) 𝜔³=1 and (2) 1+𝜔+𝜔²=0; an element of the Euclidean domain ℤ[𝜔].

To divide an Eisenstein integer a+b𝜔 by another Eisenstein integer c+d𝜔, notice that (c+d𝜔)(c+d)(c+d𝜔²)=c³+d³; accordingly multiply both denominator and numerator (of the division expressed as a fraction) by (c+d)(c+d𝜔²), then simplify.