# Gaussian integer

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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