# Gaussian integer

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Gaussian integer
A complex number where a and b are integers.

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• Gaussian integer — In number theory, a Gaussian integer is a complex number whose real and imaginary part are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as Z[i]. The… …   Wikipedia

• Gaussian integer — Math. a complex number of the form a + bi where a and b are integers. * * * …   Universalium

• gaussian integer — noun Usage: usually capitalized G : a complex number a + bi where a and b are integers and i =√‒̅1 * * * Math. a complex number of the form a + bi where a and b are integers …   Useful english dictionary

• integer — Synonyms and related words: Gaussian integer, algebraic number, article, cardinal, cardinal number, cipher, collectivity, complex, complex number, defective number, digit, embodiment, entirety, entity, even number, figure, finite number, fraction …   Moby Thesaurus

• Gaussian period — In mathematics, in the area of number theory, a Gaussian period is a certain kind of sum of roots of unity. They permit explicit calculations in cyclotomic fields, in relation both with Galois theory and with harmonic analysis (discrete Fourier… …   Wikipedia

• Gaussian elimination — In linear algebra, Gaussian elimination is an algorithm for solving systems of linear equations. It can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square… …   Wikipedia

• Gaussian beam — In optics, a Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity (irradiance) distributions are well approximated by Gaussian functions. Many lasers emit beams that approximate a Gaussian profile, in …   Wikipedia

• Gaussian integral — The Gaussian integral, or probability integral, is the improper integral of the Gaussian function e^ x}^2} over the entire real line. It is named after the German mathematician and physicist Carl Friedrich Gauss, and the equation is::int {… …   Wikipedia

• Eisenstein integer — In mathematics, Eisenstein integers, named after Ferdinand Eisenstein, are complex numbers of the form :z = a + bomega ,!where a and b are integers and:omega = frac{1}{2}( 1 + isqrt 3) = e^{2pi i/3}is a complex cube root of unity. The Eisenstein… …   Wikipedia

• Algebraic integer — This article deals with the ring of complex numbers integral over Z. For the general notion of algebraic integer, see Integrality .In number theory, an algebraic integer is a complex number which is a root of some monic polynomial (leading… …   Wikipedia