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Extended Euclidean algorithm

In arithmetic and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common divisor (gcd) of integers a and b, also the coefficients of Bézout's identity, which are integers x and y such that a x + b y = gcd ( a , b ) {\displaystyle ax+by=\gcd(a,b)} ; it is…

Standards, Computing multiplicative inverses in modular structures & Description

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Description

Polynomial extended Euclidean algorithm

Pseudocode

Computing multiplicative inverses in modular structures

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Extended Euclidean algorithm

Nodes54
Edges53
Triples22
Avg. degree1.96
Density0.037037
Components1

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Extended Euclidean algorithm

Top relations

related to Polynomial extended Euclidean algorithm · 6
Extended Euclidean algorithm → Bézout, Bézout's, Euclidean, For, Otherwise, The
related to Simple algebraic field extensions · 6
Extended Euclidean algorithm → An, Euclidean, In, The, This, Thus
related to Examples · 5
Extended Euclidean algorithm → Bézout, Euclidean, Finally, In, The
is a · 3
Extended Euclidean algorithm → essential tool for computing multiplicative inverses in modular structures, extension to the Euclidean algorithm, minimal pair of Bézout coefficients
related to Computing multiplicative inverses in modular structures · 2
Extended Euclidean algorithm → Euclidean, The

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Important terminology

displaystyle algorithm euclidean divisor greatest common extended gcd one multiplicative coprime inverse polynomial field polynomials integers two thus coefficients also

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Extended Euclidean algorithmis aextension to the Euclidean algorithm0.90text
Extended Euclidean algorithmis aminimal pair of Bézout coefficients0.90text
Extended Euclidean algorithmis aessential tool for computing multiplicative inverses in modular structures0.90text
Extended Euclidean algorithmrelated to Computing multiplicative inverses in modular structuresThe0.60section
Extended Euclidean algorithmrelated to Computing multiplicative inverses in modular structuresEuclidean0.60section
Extended Euclidean algorithmrelated to ExamplesThe0.60section
Extended Euclidean algorithmrelated to ExamplesEuclidean0.60section
Extended Euclidean algorithmrelated to ExamplesBézout0.60section
Extended Euclidean algorithmrelated to ExamplesIn0.60section
Extended Euclidean algorithmrelated to ExamplesFinally0.60section
Extended Euclidean algorithmrelated to Polynomial extended Euclidean algorithmFor0.60section
Extended Euclidean algorithmrelated to Polynomial extended Euclidean algorithmEuclidean0.60section

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