Gaussian primes - определение. Что такое Gaussian primes
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Что (кто) такое Gaussian primes - определение

COMPLEX NUMBER WHOSE REAL AND IMAGINARY PARTS ARE BOTH INTEGERS
Gauss prime; Gaussian prime; Gaussian integers; Gaussian prime number; Complex integers; Complex integer; Gaussian ring; Gaussian primes
  • ''z'' {{=}} 2 − 4''i'' ≡ −''i'' (mod ''z''<sub>0</sub>)}} is highlighted with yellow/orange dots.
  • Visualization of maximal distance to some Gaussian integer
  • Gaussian integers as [[lattice point]]s in the [[complex plane]]

Gaussian integer         
In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as .
Gaussian function         
  • The [[discrete Gaussian kernel]] (solid), compared with the [[sampled Gaussian kernel]] (dashed) for scales <math>t = 0.5,1,2,4.</math>
  • 3d plot of a Gaussian function with a two-dimensional domain
MATHEMATICAL FUNCTION
Gaussian curve; Gaussian kernel; Gauss kernel; Error Curve; Error curve; Area under Gaussian curve; Area under the bell curve; Area under gaussian curve; Gauss curve; Integral of a Gaussian function; Integral of a Gaussian Function; Gauss bell
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form
Gaussian blur         
  • This shows how smoothing affects edge detection. With more smoothing, fewer edges are detected
  • A [[halftone]] print rendered smooth through Gaussian blur
VISUAL EFFECT
Gaussian Blur; Gaussian interpolation; Gaussian smoothing; BLURRING FILTERS; Blurring technology
In image processing, a Gaussian blur (also known as Gaussian smoothing) is the result of blurring an image by a Gaussian function (named after mathematician and scientist Carl Friedrich Gauss).

Википедия

Gaussian integer

In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as Z [ i ] {\displaystyle \mathbf {Z} [i]} or Z [ i ] . {\displaystyle \mathbb {Z} [i].}

Gaussian integers share many properties with integers: they form a Euclidean domain, and have thus a Euclidean division and a Euclidean algorithm; this implies unique factorization and many related properties. However, Gaussian integers do not have a total ordering that respects arithmetic.

Gaussian integers are algebraic integers and form the simplest ring of quadratic integers.

Gaussian integers are named after the German mathematician Carl Friedrich Gauss.