See Euclidean algorithm on Wiktionary
Download JSON data for Euclidean algorithm meaning in All languages combined (5.8kB)
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"ref": "1998, John J. Roche, The Mathematics of Measurement: A Critical History, The Athlone Press, page 44",
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"text": "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,\nIn 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."
},
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"text": "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,\nIn this paper, we provide new analyses that characterize the precise average bit-complexity of a class of Euclidean algorithms.\nWe 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)."
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"ref": "2009, Brigitte Vallée, Antonio Vera, “3: Probabilistic Analyses of Lattice Reduction Algorithms”, in Phong Q. Nguyen, Brigitte Vallée, editors, The LLL Algorithm: Survey and Applications, Springer, page 71",
"text": "The general behavior of lattice reduction algorithms is far from being well understood.[…]We explain how a mixed methodology has already proved fruitful for small dimensions p, corresponding to the variety of Euclidean algorithms (p = 1) and to the Gauss algorithm (p = 2).",
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},
{
"text": "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,\nIn this paper, we provide new analyses that characterize the precise average bit-complexity of a class of Euclidean algorithms.\nWe 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)."
},
{
"ref": "2009, Brigitte Vallée, Antonio Vera, “3: Probabilistic Analyses of Lattice Reduction Algorithms”, in Phong Q. Nguyen, Brigitte Vallée, editors, The LLL Algorithm: Survey and Applications, Springer, page 71",
"text": "The general behavior of lattice reduction algorithms is far from being well understood.[…]We explain how a mixed methodology has already proved fruitful for small dimensions p, corresponding to the variety of Euclidean algorithms (p = 1) and to the Gauss algorithm (p = 2).",
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"sense": "number theory",
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"word": "euklidische Algorithmus"
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"sense": "number theory",
"tags": [
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"word": "algoritmo di Euclide"
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"word": "algoritm euclidian"
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"roman": "algorítm Jevklída",
"sense": "number theory",
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"word": "алгори́тм Евкли́да"
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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