Gaussian integer

Noun

 * 1)  Any complex number of the form a + bi, where a and b are integers.
 * 2) * 2000, André Weilert, Asymptotically fast GCD Computation in $$\mathbb{Z}[i]$$, Wieb Bosma (editor), Algorithmic Number Theory: 4th International Symposium, ANTS-IV, Proceedings, Springer, 1838, page 595,
 * We present an asymptotically fast algorithm for the computation of the greatest common divisor (GCD) of two Gaussian integers.
 * 1) * 2008, Timothy Gowers, June Barrow-Green, Imre Leader (editors), The Princeton Companion to Mathematics,, page 319,
 * For example, in the ring of Gaussian integers, $$R_{-1}$$, we have the factorizations
 * $$2 = (1+i)(1-i)$$,
 * $$5 = (1+2i)(1-2i)$$,
 * $$13 = (2+3i)(2-3i)$$,
 * $$17 = (1+4i)(1-4i)$$,
 * $$29 = (2+5i)(2-5i)$$,
 * $$\vdots$$
 * where all the Gaussian integer factors in brackets above are irreducible elements of the ring of Gaussian integers.
 * where all the Gaussian integer factors in brackets above are irreducible elements of the ring of Gaussian integers.

Hypernyms

 * algebraic integer
 * algebraic integer
 * algebraic integer