Wikipedia:Featured article candidates/Euclidean algorithm/archive1: Difference between revisions
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:As a conciliatory gesture to a numerically-minded classicist, I'll be glad to add some more references to the 130 already there. When I've finished, please reconsider your strong oppose. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 02:45, 29 April 2009 (UTC)
::I've added 22 more references. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 17:20, 30 April 2009 (UTC)
:::There are just a few more passages that I think need to be cited: 1) "However, the solutions cannot shrink indefinitely, since...." until the end. 2) "The remainder is equivalent to the congruence class in modular arithmetic." 3) "A generalization of this result is known as Sturm's theorem." 4) "Bézout's identity, and therefore the previous algorithm, can both be generalized to the context of Euclidean domains." 5) "The GCD is said to be the generator of the ideal of a and b. This GCD definition led to the modern abstract algebraic concepts of a principal ideal..." 6) "this is impossible for a system of linear equations when the solutions can be any real number." 7) "Such finite fields can be defined for any prime p; using more sophisticated definitions, they can also be defined for any power m of a prime pm. Finite fields are often called Galois fields, and are abbreviated as GF(p) or GF(pm)." 8) "Euclid's algorithm is widely used in practice, especially for small numbers, due to its simplicity. For comparison, the efficiency of alternatives to Euclid's algorithm may be determined." (statement of practice definitely needs a citation for verification) 9) "In the latter cases, the Euclidean algorithm is used to demonstrate the crucial property of unique factorization..." (see above about statements of practice) 10) "The polynomial Euclidean algorithm has other applications as well, such as Sturm chains...." 11) "Many of the other applications of the Euclidean algorithm carry over to Gaussian integers." 12) "This failure of unique factorization in some cyclotomic fields led Ernst Kummer to the concept of ideal numbers and, later, Richard Dedekind to ideals." 13) "An important generalization of the Euclidean algorithm" (characterization as "important").
:::Question - do you cite a first line, but that citation carries into the next? That could be a problem, because your citations would cover the next sentences but you don't place them where they would acknowledge that. [[User:Ottava Rima|Ottava Rima]] ([[User talk:Ottava Rima|talk]]) 14:54, 8 May 2009 (UTC)
;Comment on terminology
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