Gaussian integer
التعريفات والمعاني
== English ==
=== Noun ===
Gaussian integer (plural Gaussian integers)
(algebra) Any complex number of the form a + bi, where a and b are integers.
2000, André Weilert, Asymptotically fast GCD Computation in
Z
[
i
]
{\displaystyle \mathbb {Z} [i]}
, Wieb Bosma (editor), Algorithmic Number Theory: 4th International Symposium, ANTS-IV, Proceedings, Springer, LNCS 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, Princeton University Press, page 319,
For example, in the ring of Gaussian integers,
R
−
1
{\displaystyle R_{-1}}
, we have the factorizations
2
=
(
1
+
i
)
(
1
−
i
)
{\displaystyle 2=(1+i)(1-i)}
,
5
=
(
1
+
2
i
)
(
1
−
2
i
)
{\displaystyle 5=(1+2i)(1-2i)}
,
13
=
(
2
+
3
i
)
(
2
−
3
i
)
{\displaystyle 13=(2+3i)(2-3i)}
,
17
=
(
1
+
4
i
)
(
1
−
4
i
)
{\displaystyle 17=(1+4i)(1-4i)}
,
29
=
(
2
+
5
i
)
(
2
−
5
i
)
{\displaystyle 29=(2+5i)(2-5i)}
,
⋮
{\displaystyle \vdots }
where all the Gaussian integer factors in brackets above are irreducible elements of the ring of Gaussian integers.
==== Hypernyms ====
complex number
quadratic integer
algebraic integer
Gaussian rational number, Gaussian rational
==== Hyponyms ====
Gaussian prime
integer
==== See also ====
Eisenstein integer
Blum integer