eisenstein integer

Word Rarity Very rare

Frequency: Zipf frequency 2.32 in modern English

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Meaning

noun

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."

Named after Gotthold Eisenstein (1823–1852), German mathematician.

Eisenstein integers (plural)

Gaussian integer

Gaussian integer

Questions

What does eisenstein integer mean?

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].

Where does eisenstein integer come from?

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