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Any of certain algorithms first described in Euclid's Elements.
Definition source: English Wiktionary via Wiktextract
Usage: historical
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
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.
Definition source: English Wiktionary via Wiktextract
Topics: arithmetic, mathematics, number-theory, sciences
Examples
- 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, LNCS 204, page 279, In a quadratic field Q (√), 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<-19 even remainder sequences with possibly nondecreasing norms cannot determine the GCD of arbitrary inputs.
- 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, LNCS 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 (G), By-Excess (L), Centered (K), Subtractive (T) and Binary (B).
Meaning relationships
Synonyms: none provided
Antonyms: none provided
No etymology was provided for this word.
Across languages
Translations
11 source translations are retained for this English entry.
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Bulgarian:
алгоритъм на Евклид
(algoritǎm na Evklid)
— number theory
-
Czech:
Euklidův algoritmus
— number theory
-
Finnish:
Eukleideen algoritmi
— number theory
-
French:
algorithme d'Euclide
— number theory
-
German:
euklidische Algorithmus
— number theory
-
Hungarian:
euklideszi algoritmus
— number theory
-
Icelandic:
reiknirit Evklíðs
— number theory
-
Italian:
algoritmo di Euclide
— number theory
-
Romanian:
algoritm euclidian
— number theory
-
Russian:
алгори́тм Евкли́да
(algorítm Jevklída)
— number theory
-
Spanish:
algoritmo de Euclides
— number theory
