Eisenstein integer en · NOUN
Etymology
Named after Gotthold Eisenstein (1823–1852), German mathematician.
Meanings
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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#43;b#92;omega by another Eisenstein integer c#43;d#92;omega, notice that (c#43;d#92;omega)(c#43;d)(c#43;d#92;omega²)#61;c³#43;d³; accordingly multiply both denominator and numerator (of the division expressed as a fraction) by (c#43;d)(c#43;d#92;omega²), then simplify.
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| Eisenstein integers | Number=Plur | lexicographic |
Hypernyms
quadratic integer · algebraic integer