Euclidean algorithm

Noun

 * 1)  Any of certain algorithms first described in.
 * 2)  Specifically, a method, based on a division algorithm, for finding the greatest common divisor (gcd) of two given integers; any of certain variations or generalisations of said method.
 * 3) * 1985, Erich Kaltofen, Heinrich Rolletschek, Arithmetic in Quadratic Fields with Unique Factorization, Bob F. Caviness (editor), EUROCAL '85, European Conference on Computer Algebra, Linz, Proceedings, Volume 2, Springer, 204, page 279,
 * In a quadratic field $$\Q(\sqrt{D})$$, $$D$$ a squarefree integer, with class number 1 any algebraic integer can be decomposed uniquely into primes but for only 21 domains Euclidean algorithms are known. We prove that for $$D\le -19$$ even remainder sequences with possibly nondecreasing norms cannot determine the GCD of arbitrary inputs.
 * 1) * 2003, Ali Akhavi, Brigitte Vallée, Average Bit-Complexity of Euclidean Algorithms, Ugo Montanari, Jose D.P. Rolim, Emo Welzl (editors), Automata, Languages and Programming: 27th International Colloquium, Proceedings, Springer, 1853, page 373,
 * In this paper, we provide new analyses that characterize the precise average bit-complexity of a class of Euclidean algorithms.
 * We consider here five algorithms that are all classical variations of the Euclidean algorithm and are called Classical ($$\mathcal{G}$$), By-Excess ($$\mathcal{L}$$), Centered ($$\mathcal{K}$$), Subtractive ($$\mathcal{T}$$) and Binary ($$\mathcal{B}$$).
 * We consider here five algorithms that are all classical variations of the Euclidean algorithm and are called Classical ($$\mathcal{G}$$), By-Excess ($$\mathcal{L}$$), Centered ($$\mathcal{K}$$), Subtractive ($$\mathcal{T}$$) and Binary ($$\mathcal{B}$$).

Translations

 * Czech: Euklidův algoritmus
 * Finnish: Eukleideen algoritmi
 * French: algorithme d'Euclide
 * German: euklidische Algorithmus
 * Hungarian:
 * Icelandic: reiknirit Evklíðs
 * Italian: algoritmo di Euclide
 * Romanian: algoritm euclidian
 * Russian: алгори́тм Евкли́да
 * Spanish: algoritmo de Euclides