Gaussian integer

English

Noun

1. Template:Lb Any complex number of the form a + bi, where a and b are integers.
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   • 2000, André Weilert, Asymptotically fast GCD Computation in $\mathbb{Z}[i]$, Wieb Bosma (editor), Algorithmic Number Theory: 4th International Symposium, ANTS-IV, Proceedings, Springer, Template:W 1838, page 595,

     We present an asymptotically fast algorithm for the computation of the greatest common divisor (GCD) of two Gaussian integers.

   • 2008, Timothy Gowers, June Barrow-Green, Imre Leader (editors), The Princeton Companion to Mathematics, Template:W, page 319,

     For example, in the ring of Gaussian integers, $R_{-1}$, we have the factorizations

     $2=(1+i)(1-i)$,

     $5=(1+2i)(1-2i)$,

     $13=(2+3i)(2-3i)$,

     $17=(1+4i)(1-4i)$,

     $29=(2+5i)(2-5i)$,

     $⋮$

     where all the Gaussian integer factors in brackets above are irreducible elements of the ring of Gaussian integers.

Hypernyms

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  • algebraic integer
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Hyponyms

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See also

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